Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

Organizations enter alliances with each other to access critical resources, but they rely on information from the network of prior alliances to determine with whom to cooperate. These new alliances modify the existing network, prompting an endogenous dynamic between organizational action and network structure that drives the emergence of interorganizational networks. Testing these ideas on alliances formed in three industries over nine years, the authors show that the probability of a new alliance between specific organizations increases with their interdependence, but also with their prior mutual alliances, common third parties, and joint centrality in the alliance network. The differentiation of the emerging network structure, however, mitigates the effect of interdependence and enhances the effect of joint centrality on new alliance formation.

Abstract Betweenness is a measure of the centrality of a node in a network, and is normally calculated as the fraction of shortest paths between node pairs that pass through the node of interest. Betweenness is, in some sense, a measure of the influence a node has over the spread of information through the network. By counting only shortest paths, however, the conventional definition implicitly assumes that information spreads only along those shortest paths. Here, we propose a betweenness measure that relaxes this assumption, including contributions from essentially all paths between nodes, not just the shortest, although it still gives more weight to short paths. The measure is based on random walks, counting how often a node is traversed by a random walk between two other nodes. We show how our measure can be calculated using matrix methods, and give some examples of its application to particular networks.

Sociological investigations of economic exchange reveal how institutions and social structures shape transaction patterns among economic actors. This article explores how interfirm networks in the U.S. venture capital (VC) market affect spatial patterns of exchange. Evidence suggests that information about potential investment opportunities generally circulates within geographic and industry spaces. In turn, the circumscribed flow of information within these spaces contributes to the geographic- and industry-localization of VC investments. Empirical analyses demonstrate that the social networks in the VC community—built up through the industry’s extensive use of syndicated investing—diffuse information across boundaries and therefore expand the spatial radius of exchange. Venture capitalists that build axial positions in the industry’s coinvestment network invest more frequently in spatially distant companies. Thus, variation in actors ’ positioning within the structure of the market appears to differentiate market participants ’ ability to overcome boundaries that otherwise would curtail exchange.

Abstract Data on social networks may be gathered for all ties linking elements of a closed population ("complete" network data) or for the sets of ties surrounding sampled individual units ("egocentric" network data). Network data have been obtained via surveys and questionnaires, archives, observation, diaries, electronic traces, and experiments. Most methodological research on data quality concerns surveys and questionnaires. The question of the accuracy with which informants can provide data on their network ties is nontrivial, but survey methods can make some claim to reliability. Unresolved issues include whether to measure perceived social ties or actual exchanges, how to treat temporal elements in the definition of relationships, and whether to seek accurate descriptions or reliable indicators. Continued research on data quality is needed; beyond improved samples and further investigation of the informant accuracy/reliability issue, this should cover common indices of network structure, address the consequences of sampling portions of a network, and examine the robustness of indicators of network structure and position to both random and nonrandom errors of measurement.

Centrality measures, or at least our interpretations of these measures, make implicit assumptions about the manner in which things flow through a network. For example, some measures count only geodesic paths, apparently assuming that whatever flows through the network only moves along the shortest possible paths. This paper lays out a typology of network flows based on two dimensions of variation, namely, the kinds of trajectories that traffic may follow (geodesics, paths, trails or walks), and the method of spread (broadcast, serial replication, or transfer). Measures of centrality are then matched to the kinds of flows they are appropriate for. Simulations are used to examine the relationship between type of flow and the differential importance of nodes with respect to key measurements such as speed of reception of traffic and frequency of receiving traffic. It is shown that the off-the-shelf formulas for centrality measures are fully applicable only for the specific flow processes they are designed for, and that when they are applied to other flow processes they get the “wrong” answer. It is noted that the most commonly used centrality measures are not appropriate for most of the flows we are routinely interested in. A key claim made in this paper is that centrality measures can be regarded as generating expected values for certain kinds of node outcomes (such as speed and frequency of reception) given implicit models of how things flow.

A common but informal notion in social network analysis and other fields is the concept of a corerperiphery structure. The intuitive conception entails a dense, cohesive core and a sparse, unconnected periphery. This paper seeks to formalize the intuitive notion of a corerperiphery structure and suggests algorithms for detecting this structure, along with statistical tests for testing a priori hypotheses. Different .models are presented for different kinds of graphs directed and undirected, valued and nonvalued. In addition, the close relation of the continuous models developed to certain centrality measures is discussed.

Abstract Many financial markets are characterized by strong relationships and networks, rather than arm's-length, spot-market transactions. We examine the performance consequences of this organizational choice in the context of relationships established when VCs syndicate portfolio company investments, using a comprehensive sample of U.S. based VCs over the period 1980 to 2003. VC funds whose parent firms enjoy more influential network positions have significantly better performance, as measured by the proportion of portfolio company investments that are successfully exited through an initial public offering or a sale to another company. Similarly, the portfolio companies of better networked VC firms are significantly more likely to survive to subsequent rounds of financing and to eventual exit. The magnitude of these effects is economically large, and is robust to a wide range of specifications. Once we control for network effects in our models of fund and portfolio company performance, the importance of how much investment experience a VC has is reduced, and in some specifications, eliminated. Finally, we provide initial evidence on the evolution of VC networks. Key words: Venture Capital, Networks, Syndication, Investment Performance JEL classification: G24, L14. Networks are widespread in many financial markets. Bulge-bracket investment banks, for instance, have strong relationships with institutional investors which they make use of when pricing and distributing corporate securities (Benveniste and Spindt (1989), Cornelli and Goldreich (2001)). In the corporate loan market, banks often prefer syndicating loans with other banks over being the sole lender. Similarly, in the primary equity and bond markets, banks tend to co-underwrite securities offerings with banks they have long-standing relationships with (Corwin and Schultz (2005)). In the same spirit, networks feature prominently in the venture capital industry. VCs tend to syndicate their investments with other VCs, rather than investing alone (Lerner (1994a)). They are thus bound by their current and past investments into webs of relationships with other VCs. Once they have invested in a company, VCs draw on their networks of service providers -head hunters, patent lawyers, investment bankers etc. -to help the company succeed (Gorman and Sahlman (1989), While the prevalence of networking in many financial markets has been documented in the literature, the performance consequences of this organizational choice remain unknown. In the venture capital market, for instance, some VCs presumably have better-quality relationships and hence enjoy more influential network positions than others, implying differences in their clout, investment opportunity sets, access to information, etc. In this study, we ask whether these differences help explain the cross-section of VC investment performance. We focus on the co-investment networks that VC syndication gives rise to, and leave the other two main networks VCs use (involving service providers and institutional investors in their funds) to future research. Syndication relationships are a natural starting point, not only because they are easy to observe, but also because there are good reasons to believe they are vital to a VC's performance. The two main drivers of a VC's performance are the ability to source high-quality deal flow (i.e., the ability to select promising companies), and the ability to nurture its investments (i.e., the ability to add value to portfolio companies). Syndication likely affects both of these performance drivers. 2 There are at least three reasons to expect syndication networks to improve the quality of deal flow. First, VCs invite others to co-invest in their promising deals in expectation of future reciprocity (Lerner (1994a)). Second, by checking each other's willingness to invest in potentially promising deals, VCs can pool correlated signals and thereby may select better investments in situations of often extreme uncertainty about the viability and return potential of investment proposals (Wilson (1968), Third, individual VCs tend to have investment expertise that is both sector-specific and location-specific. Syndication helps diffuse information across sector boundaries and expands the spatial radius of exchange, thus allowing VCs to diversify their portfolios In addition to improving deal flow, syndication networks may also help VCs add value to their portfolio companies. 1 Syndication networks facilitate the sharing of information, contacts, and resources among VCs (Bygrave (1988)), for instance by expanding the range of strategic alliance partners and launch customers for their portfolio companies. No less importantly, strong relationships with other VCs likely improve the chances of securing follow-on VC funding for portfolio companies, and may indirectly provide access to other VCs' relationships with service providers such as head hunters and prestigious investment banks. An examination of the performance consequences of VC networks requires measures of how well networked a VC is. We borrow these measures from graph theory, a mathematical discipline widely used in economic sociology. 2 Graph theory provides us with tools for describing networks at a "macro" level and for measuring the relative importance, or "centrality," of each actor in the network. Our centrality measures capture five different aspects of a VC firm's influence: The number of VCs it has relationships with, as a proxy for the information, deal flow, expertise, contacts, and pools of capital it has access to; the frequency with which it is invited to co-invest in other VCs' deals, thereby expanding its investment opportunity set; its ability to generate such co-investment opportunities in the future by syndicating its own deals today in the hope of future payback from its syndication partners; its access to the best-connected VCs; and its 1 The literature has documented a number of ways in which VCs add value to their portfolio companies, such as addressing weaknesses in the original business plan or the entrepreneurial team (Kaplan and Strömberg (2004)), professionalizing the company (Hellmann and Puri In addition to measures of how well networked each VC is, we require data on the performance of VC investments. We examine both the performance of the VC fund and of the fund's portfolio companies. At the fund level, we examine "exit rates" in the absence of publicly available data on VC fund returns. We define a fund's exit rate as the fraction of portfolio companies that are successfully exited via an initial public offering (IPO) or a sale to another company. At the portfolio company level, we examine not only whether or not the portfolio company achieved a successful exit, but also intermediate performance, namely whether the portfolio company survived to obtain an additional round of funding. Controlling for other known determinants of VC fund performance such as fund size (Kaplan and Schoar When we examine performance at the portfolio company level, we find that a VC's network centrality has a positive and significant effect on the probability that a portfolio company survives to a subsequent funding round or exits successfully. This effect is large economically. For instance, the survival probability in the first funding round increases from the unconditional expectation of 66.8% to 72.4% for a onestandard-deviation increase in the lead VC's network centrality. Perhaps the leading alternative explanation for the performance-enhancing role of VC networking is simply experience (e.g., Kaplan, Martel, and Strömberg (2003)). It seems plausible that the better-4 networked VCs are also the older and more experienced VCs. To rule out that our measures of network centrality merely proxy for experience, our models explicitly control for a variety of dimensions of VC experience. Interestingly, once we control for VC networks, the beneficial effect of experience on performance is reduced, and in some specifications, eliminated. It is also not the case that the betternetworked VCs are simply the ones with better past performance records: While we do find evidence of persistence in performance from one fund to the next, our measures of network centrality continue to have a positive and significant effect on fund exit rates when we control for persistence. The way we construct the centrality measures makes it unlikely that our results are driven simply by reverse causality (that is, the argument that superior performance enables VCs to improve their network positions, rather than the other way around). For a fund of a given vintage year, measures of network centrality are constructed from syndication data for the five preceding years. Performance is then taken as the exit rate over the life of the fund, which lasts 10-12 years. Thus, we are relating a VC firm's past network position to its future performance. Moreover, we find little evidence that past exits drive future network position. Instead, what appears to be key in improving a VC firm's network position is demonstrating skill in selecting, and adding value to, investments. We also explore an alternative explanation for the positive relation between exit rates and network centrality, namely that better networked VCs may simply be better at hoodwinking the public markets into buying their more marginal companies, but find little support for this explanation. Our main results are based on centrality measures derived from syndication networks that span all industries and the entire United States. To the extent that VC networks are geographically concentrated or industry-specific, this may underestimate a VC's network centrality. We therefore repeat our analysis using industry-specific networks and a separate network of VC firms in California, the largest VC market in the U.S. Our results are not only robust to these modifications, but their economic significance increases substantially. In the California network, exit rates improve by approximately five percentage points relative to the unconditional mean of 35.7% among California VCs. Our contribution is fivefold. This is the first paper to examine the performance consequences of the VC industry's predominant choice of organizational form: Networks. Previous work has focused on describing the structure of syndication networks (Bygrave (1987(Bygrave ( , 1988, The remainder of the paper is organized as follows. Section I provides an overview of network analysis techniques and discusses their implementation in the VC context. A simple example illustrating network analysis is presented in the Appendix. Section II describes our data. In Section III, we analyze the effect of VC networking on fund performance. Section IV examines the relation between networking and portfolio company survival. Section V presents additional robustness checks, including an examination of the effects of industry-specific and spatially separated networks. Section VI investigates how a VC becomes influential in the VC network. Section VII concludes. I. Network Analysis Methodology The aim of network analysis is to describe the structure of networks, by focusing first and foremost on the relationships that exist among a set of economic actors and less on the individual actors' characteristics (such as age, wealth, etc.). For instance, a network might be described as "dense" (if many actors are tied to one another via reciprocated relationships) or "sparse" (if actors tend to be more autarkic). It might have one dense area surrounded by a periphery of sparsely connected actors, or it might have several clusters of dense areas that occasionally interact with each other. The network might be populated by uniformly influential actors, or there may be variation in actors' influence. And so on. Influence is usually measured by how "central" an actor's network position is. An actor is considered central if he is extensively involved in relationships with other actors. Consider the most centralized of networks, the "star," in which one actor is connected to all other actors, none of whom is connected to 6 anyone else. Clearly, the actor at the center of the star is the most influential. Contrast this with a ringshaped network, in which all actors are equally central. In the VC market, greater centrality may translate into better access to information, deal flow, deeper pools of capital, expertise, contacts, and so on. Network analysis uses a branch of mathematics called graph theory to make the concept of centrality more precise. 3 Consider the network illustrated in In graph theory, a network such as the one illustrated in 6 Networks are not static. Relationships may change, and entry to and exit from the network may change each actor's centrality. We therefore construct our adjacency matrices over trailing five-year windows. Using these matrices, we construct five centrality measures based on three popular concepts of centrality: Degree, closeness, and betweenness. Using a numerical example, the Appendix shows in detail how these centrality measures are constructed. Here, we focus on how each measure captures a slightly different aspect of a VC's economic role in the network. 3 See Wasserman and Faust (1997) for a detailed review of network analysis methods. 4 For tractability, the graph excludes biotech-focused VC firms that have no syndication relationships during this period. 5 As the example in the Appendix illustrates, this method of coding ties produces a binary adjacency matrix. It is possible to construct a valued adjacency matrix accounting not only for the existence of a tie between two VCs but also for the number of times there is a tie between them. While the results reported in the following sections utilize the binary matrix, we note that all our results are robust to using network centrality measures calculated from valued matrices. 6 Unlike the undirected matrix, the directed matrix does not record a tie between VCs j and k who were members of the same syndicate if neither led the syndicate in question. Indegree is a measure of the frequency with which a VC firm is invited to co-invest in other VCs' deals, thereby expanding its investment opportunity set and gaining access to information and resources it otherwise may not have had access to. Formally, let q ji be an indicator equaling one if at least one syndication relationship exists in which VC j was the lead investor and VC i was a syndicate member, and zero otherwise. VC i's indegree then equals Σ i q ji . Outdegree is a measure of a VC's ability to generate future co-investment opportunities by inviting others into its syndicates today (i.e., reciprocity). Outdegree counts the number of other VCs a VC firm invites into its own syndicates. Formally, as before, let q ij be an indicator equaling one if at least one syndication relationship exists in which VC i was the lead investor and VC j was a syndicate member, and zero otherwise. VC i's outdegree then equals Σ j q ij . Clearly, all three degree centrality measures are a function of network size, which in our dataset varies over time due to entry and exit by VCs. To ensure comparability over time, we normalize each degree centrality measure by dividing by the maximum possible degree in an n-actor network (i.e., n-1). While we normalize the centrality measures used in the empirical analysis, we note that all our results are robust to using non-normalized network centrality measures instead. 8 B. Closeness While degree counts the number of relationships an actor has, closeness takes into account their "quality." A particularly useful measure of closeness is "eigenvector centrality" (Bonacich (1972(Bonacich ( , 1987), which weights an actor's ties to others by the importance of the actors he is tied to. In essence, eigenvector centrality is a recursive measure of degree, whereby the centrality of an actor is defined as the sum of his ties to other actors, weighted by their respective centralities. Formally, let p ij be an indicator equaling one if at least one syndication relationship exists between VC i and VC j, and zero otherwise. VC i's eigenvector centrality is then defined as ev i = Σ j p ij ev j (which is equivalent to the components of the principal eigenvector of the adjacency matrix). 8 In our setting, eigenvector centrality measures the extent to which a VC is connected to other well-connected VCs. This is normalized by the highest eigenvector centrality measure possible in a network of n actors. C. Betweenness Centrality Betweenness attributes influence to actors on whom many others must rely to make connections within the network. For example, in a star, the actor at the center stands between every pair of actors, who must involve him to reach one another. In our setting, betweenness proxies for the extent to which a VC may act as an intermediary by bringing together VCs with complementary skills or investment opportunities who lack a direct relationship between them. Formally, let b jk be the proportion of all paths linking actors j and k which pass through actor i. The betweenness of actor i is defined as the sum of all b jk where i, j, and k are distinct. It is normalized by dividing by the maximum betweenness in an n-actor network. II. Sample and Data Data for our analysis are obtained from Thomson Financial's Venture Economics database. Venture Economics began compiling data on venture capital investments in 1977, and has since backfilled the data to the early 1960s. Gompers and Lerner (1999) investigate the completeness of the Venture Economics database and conclude that it covers more than 90% of all venture investments. Most VC funds are structured as closed-end, often ten-year, limited partnerships. They are not stock 8 Formally, given an adjacency matrix A, the eigenvector centrality of actor i is given by ev i =a∑A ij ev j where a is a parameter required to give the equations a non-trivial solution (and is therefore the reciprocal of an eigenvalue). As the centrality of each actor is determined by the centrality of the actors he is connected to, the centralities will be the elements of the principal eigenvector. We concentrate solely on investments by U.S. based VC funds, and exclude investments by angels and buyout funds. 10 We distinguish between funds and firms. While VC funds have a limited (usually ten-year) life, the VC management firms that manage the funds have no predetermined lifespan. A first-time fund that is successful often enables the VC firm to raise a follow-on fund (Kaplan and Schoar 12 For the remaining undirected centrality measures, we are primarily interested in the ties among VCs instanced by co-investment in the same portfolio company. Here, we are less concerned with whether the co-investment occurred in the same financing round or in different rounds, because we assume VC relationships are built by interacting with one another in board meetings and other activities that help the portfolio company succeed. Thus, a VC who invested in the company's first round may interact with a VC who joined in the second round. To capture this, we examine syndicates at the company level and define the syndicate as the collection of VC firms that invested in a given portfolio company. All our results are robust, both in terms of economic and statistical significance, to employing either definition of syndicate for both the directed and undirected centrality measures. A. Fund Characteristics 11 Many VCs specialize in a particular industry, and important performance drivers such as investment opportunities and competition for deal flow likely vary across industries. Venture Economics does not identify which industry a fund specializes in, but it classifies the funds' portfolio companies into six broad groups. We take a sample fund's industry specialization to be the broad Venture Economics industry group that accounts for most of its invested capital. On this basis, 46.2% of funds specialize in "Computer related" companies, 18.9% in "Non-high-technology," 9.2% in "Medical, health, life sciences," 15.5% in "Communications and media," 6% in "Biotechnology," and 4.3% in "Semiconductors, other electronics." B. Measuring Fund Performance Ideally, we would measure fund performance directly, using for instance the internal rate of return a fund achieved over its ten-year life. However, fund returns in the form required for this study are not systematically available to researchers as VC funds generally do not disclose their performance to anyone other than their own investors. Venture Economics collects fund performance data from VC investors, but only makes them publicly available in aggregate form (e.g., "the median IRR for funds raised in 1993 was..."). Some researchers have recently had access to disaggregated performance data from Venture Economics, but only in anonymized format (see Kaplan and Schoar (2005); Jones and Rhodes-Kropf Instead, we measure fund performance indirectly. Ljungqvist and Richardson (2003) report that 75.3% of investments are written off completely in the average VC fund in their sample. This implies that VC funds earn their capital gains from a small subset of their portfolio companies, namely those that they exit via an IPO or a sale to another company (M&A). 13 All else equal, the more successful exits a fund has, the larger will be its IRR. Thus, we take as our main proxy for VC fund performance the fraction of the fund's portfolio companies that have been successfully exited via an IPO or M&A transaction, as identified in the Venture Economics database as of November 2003. In Section III.E, we show that this is a reasonable proxy for fund returns. 13 Unsuccessful investments are typically shut down or sold to management for a nominal sum. 12 This could be because they have yet to complete their ten-year investment lives. Alternatively, the deterioration in the investment climate and, especially, in the IPO market since the ending of the dot-com and technology booms of the late 1990s may result in these funds never matching the performance of earlier VC vintages. Whatever the reason, to capture the pronounced time pattern evident in C. Company-level Performance Measures Data limitations prevent us from computing company-level rates of return: The Venture Economics database does not include details on the fraction of equity acquired by the VCs or the securities they hold, and occasionally lacks information even on the amount invested. 14 Instead, we use two indirect measures of company-level performance. Most venture-backed investments are "staged" in the sense that portfolio companies are periodically reevaluated and receive follow-on funding only if their prospects remain promising (Gompers (1995)). Thus, we view survival to another funding round as an interim signal of success. Eventually, successful portfolio companies are taken public or sold. Absent return data, we follow Gompers and Lerner (1998, 2000), Brander, Amit, and Antweiler (2002) and D. VC Firm Experience Kaplan and Schoar E. Network Measures Over our sample period, the VC industry saw substantial entry and exit and thus a considerable reordering of relationships. To capture the dynamics of these processes, we construct a new network for each year t, using data on syndications from the five years ending in t. 18 Within each of these five-year windows, we make no distinction between relationships reflected in earlier or later syndicates. We then use the resulting adjacency matrices to construct the five centrality measures described in Section I. The parent of the average sample fund has normalized outdegree of 1.203%, indegree of 1.003%, and degree of 4.237% (see To illustrate the variation in the degree measures, we consider the extremes. Over the five years ending in 1999, New Enterprise Associates syndicated with the largest number of VCs (369). By contrast, 186 (10.3%) of the 1,812 VC firms active in the market during the 1995-1999 window never syndicated any investments, preferring instead to invest on their own. Betweenness and eigenvector centrality average 0.29% and 3.74% of their respective theoretical maximum. Throughout most of the 1990s, New Enterprise Associates had the highest betweenness centrality scores (standing "between" approximately 6% of all possible VC pairs), only to be overtaken by Intel Capital, the venture capital arm of Intel Corp, in 1999. 17 Since Venture Economics' data are somewhat unreliable before 1980, we ignore investments dated earlier than 1975. This coding convention does not affect our results. 18 All our results are robust to using three-, seven-, or ten-year windows instead, with shorter windows generally being associated with stronger effects. Overall, VC syndication networks are not particularly dense. As a proportion of all the relationships between every pair of VCs that could be present, the density of undirected ties peaked at 4.5% in 1987-1991 and has been declining to below 2% since. Directed ties (i.e., those between lead VC and syndicate members) are even less dense. In part, this simply reflects the large number of VCs and the tendency of some VCs never to syndicate their investments, 19 but it likely also reflects the aforementioned exclusivity and repeated nature of syndication relationships evident in the low individual degree centrality scores. 15 F. The Macro Structure of VC Networks Low density can suggest high centralization. A simple way to measure the overall centralization of a network (as opposed to the centrality of individual actors) is to express the network-wide variation in the actors' degree, betweenness, and eigenvector centralities as a percentage of the variation we would observe in the most centralized network, a perfect star, of equivalent size. The resulting centralization numbers can be interpreted as measures of the degree of inequality in the network. As G. Competition for Deal Flow and Investment Opportunities Our models include a range of control variables. Gompers and Lerner (2000) show that the prices VCs pay when investing in portfolio companies increase as more money flows into the VC industry, holding investment opportunities constant. They interpret this pattern as evidence that competition for scarce investment opportunities drives up valuations. If so, it seems plausible that competition for deal flow also affects the quality of VCs' investments and thus their performance. We therefore include in our fund-level 19 All our results are robust to excluding VC firms that never syndicate. 16 and company-level models the aggregate VC fund inflows in the year a sample fund was raised and the year a portfolio company completed a funding round, respectively. Controlling for the investment opportunities open to a VC is harder. Gompers and Lerner 21 VC funds take a number of years to invest their available capital. Thus, we have to decide over what time period to measure their investment opportunities. For the purpose of the fund-level analyses in Section III, we average B/M and P/E ratios over each fund's first three years of existence, to approximate its active investment period. Results are robust to using longer or shorter windows. 20 Similar results are obtained when using three-digit SIC codes. 21 We define a public company's P/E ratio as the ratio of stock price (COMPUSTAT data item #199) to earnings-per-share excluding extraordinary items (#58). We define the B/M ratio as the ratio of book equity to market equity, where book equity is defined as total assets (#6) minus liabilities (#181) minus preferred stock (#10, #56, or #130, in order of availability) plus deferred tax and investment tax credit (#35), and market equity is defined as stock price (#199) multiplied by shares outstanding (#25). To control for outliers, we follow standard convention and winsorize the P/E and B/M ratios at the 5 th and 95 th percentiles for the universe of firms in COMPUSTAT in that year. (The results are robust to other winsorization cutoffs.) To calculate a value-weighted average, we consider as weights both the firm's market value (market value of equity plus liabilities minus deferred tax and investment tax credit plus preferred stock) and the dollar amount of investment in each four-digit SIC code each year (as calculated from the Venture Economics database). 17 III. Fund-level Analysis A. Benchmark Determinants of Fund Performance We begin by replicating Kaplan and Schoar's (2005) fund performance model, to validate our use of exit rates instead of fund returns as the measure of performance. Kaplan and Schoar relate VC fund performance to two fund characteristics (as well as a set of vintage year dummies): Log fund size and log fund sequence number, each of which is included in levels and squares. Our results are reported in 22 Consistent with Kaplan and Schoar, we find only weak evidence that higher sequence number funds perform better (p=0.099) once we exclude fund size in column (2), and strong evidence that larger funds perform significantly better (p<0.001) once we exclude fund sequence number in column (3). As in Kaplan and Schoar (whose dataset is a subset of ours), the relation between fund performance and fund size is increasing and concave, consistent with diminishing returns to scale. The adjusted R 2 in model (3) is 13.6%. Because fund sequence number appears to have little effect on fund performance in our dataset, and because it is frequently unavailable in the Venture Economics database, we replace it with a dummy equaling one for first-time funds. We also control for funds that Venture Economics classifies as seed or early-stage funds, on the assumption that such funds invest in riskier companies and so have relatively fewer successful exits. The resulting model is shown in column (4). In addition to the positive and concave effect of fund size, we find that first-time funds perform significantly worse, mirroring Kaplan and Schoar's (2005) results: All else equal, first-time funds have exit rates that are 3.6 percentage points below average (that is, 30.9% rather than 34.5%). In this specification, seed and early-stage funds do not perform differently from other funds. The model shown in column (5) adds the log of vintage-year VC fund inflows in an attempt to control for Gompers and Lerner's (2000) "money chasing deals" result, whereby inflows of capital into VC funds increase the competition for a limited number of attractive investment opportunities. Consistent with the 22 It is difficult to control directly for exit market conditions over the life of a fund, as market conditions may vary widely over the 7+ years in which portfolio companies are likely to reach exit stage. The year fixed effects may help control for heterogeneity in exit rates related to the fund's vintage year timing (and hence subsequent exit market conditions). See Section IV.C for company-level models that control explicitly for exit market conditions. 18 spirit of their results, we find that funds subsequently perform significantly worse the more money flowed into the VC industry in the year they were raised. The effect is large economically: A one-standarddeviation increase in vintage-year fund inflows reduces exit rates by seven percentage points from the 34.5% estimation sample average, holding all other covariates at their sample means. Columns (6) and B. The Effect of Firm Experience on Fund Performance From now on, we take the model shown in column (7) of However we measure it, funds with more experienced parents perform significantly better. Onestandard-deviation increases in the log number of days since the parent's first-ever investment, the log number of rounds the parent has participated in, the log aggregate amount it has invested, and the log number of portfolio companies it has funded, each measured up to the year the VC fund was raised, increase exit rates by 3.7, 3.5, 4.4, and 3.3 percentage points, respectively. Note that the first-fund dummy loses significance in these models, indicating that it is a poor proxy for experience. Since the log aggregate investment amount proxy has the largest economic effect, we will use it in all subsequent models to proxy for the parent firm's experience. Our results are generally robust to using any of the other three proxies instead. C. The Effect of Firm Networks on Fund Performance Having controlled for fund characteristics, competition for deal flow, investment opportunities, and 19 parent firm experience, does a VC's network centrality (measured over the prior five years) improve the performance of its fund (over the next ten years)? The results, shown in We estimate five separate regression models, adding our five centrality measures to the specification shown in column (3) of 24 Of the five network measures, eigenvector has the largest economic effect, closely followed by degree and indegree. To illustrate, a one-standard-deviation increase in these measures is associated with a more than two percentage point increase in exit rates, all else equal. Thus, a VC benefits from having many ties (degree), especially when the ties involve other well-connected VCs (eigenvector), and from being invited into many syndicates (indegree). Having the ability to act as a broker between other VCs (betweenness) has a smaller effect, with a one-standard-deviation increase in this centrality measure being associated with only a one percentage point increase in fund performance. This will prove to be true throughout our analysis, suggesting that indirect relationships (those requiring intermediation) play a lesser role in the venture capital market. Similarly, outdegree has a relatively small effect economically, which is consistent with the view that this measure captures a VC firm's investment in future reciprocity, which takes some time to pay off. In other words, inviting many VCs into one's syndicates today (i.e., high outdegree) will hopefully result in many co-investment opportunities for one's future funds (i.e., high future indegree). We will explore this dynamic relation between indegree and outdegree further in Section VI. D. Reverse Causality and Performance Persistence We do not believe that our results are driven simply by reverse causality, i.e., that a higher fund exit rate enables a VC to improve its network position, rather than the other way around. Recall that we construct the network centrality measures from syndication data for the five years before a fund is created. The fact that these data can help explain fund performance over the next ten years suggests that networking 23 One obvious concern is that our network centrality measures merely proxy for (or are cleaner measures of) VC parent firm experience. However, the pairwise correlations between the experience measure and the five measures of network centralities are relatively low, ranging from 36.8% to 43.9%. 24 If we restrict the sample to funds raised prior to 1995, to ensure each sample fund has completed its ten-year life, betweenness and outdegree cease to be significant at conventional levels. Indegree, degree, and eigenvectors continue to be positively and significantly related to fund performance. 20 truly affects performance. A potentially more serious concern is persistence in performance from fund to fund. To rule out that the network measures are simply proxying for omitted persistence in performance, we re-estimate our fundlevel models including among the regressors the exit rate of the VC firm's most recent past fund. Note that this restricts our sample to VC firms that have raised at least two funds between 1980 and 1999; first-time funds and VC firms that do not raise follow-on funds are necessarily excluded. 25 The results are shown in E. Exit Rates and Internal Rates of Return To ascertain the extent to which our measure of fund performance, exit rates, relates to fund returns, we use a sample of fund IRRs recently disclosed by public pension plans and state universities following Freedom of Information Act suits. Such data are available for 188 of the 3,469 funds in our sample. While this sample is small and not necessarily representative, it provides us with an opportunity to partially examine the relation between exit rates and IRRs and thus the robustness of our fund performance results. The correlation between exit rates and IRRs is 0.42 (p<0.001), suggesting that exit rates are a useful but noisy proxy for IRRs. We re-estimate our fund-level performance models on the subsample of funds for which IRRs are available. (To conserve space, the results are not reported in tables.) This both weakens and strengthens our results. On the one hand, the coefficients estimated for outdegree, degree, and betweenness are no longer statistically significant. On the other, the coefficient estimates for indegree and eigenvector 25 We obtain similar (and somewhat stronger) results if we include all funds, setting the prior performance variable equal to zero for first-time funds and including a dummy variable identifying first-time funds. 21 are not only statistically significant, they are also very large economically: IRRs increase by between 11 and 14 percentage points from the 15% sample average for one-standard-deviation increases in indegree and eigenvector. The adjusted R 2 s in all five models are high, ranging from 27.8% for the outdegree specification to 30% for the eigenvector specification. Finally, we regress IRRs on exit rates to help interpret economic significance in our exit rate models (results not shown). On average, funds break even (i.e., IRR=0) at an exit rate of 18.8%. Beyond 18.8%, each 1% increase in exit rates is associated with a 1.046% increase in IRRs (p<0.001). If we are willing to assume that the relation between IRRs and exit rates remains roughly one-to-one in the overall sample (for which we do not have IRR data), this suggests that we can translate the economic significance exercises in the previous sections into IRR gains on nearly a one-for-one basis. In other words, a two percentage point increase in exit rates (from the mean of around 35%) is roughly equivalent to a two percentage point increase in IRR (from a mean of around 15%). IV. Company-level Analysis We now turn to estimating the effect of VC networking on portfolio company performance. In the absence of company-level rates of return data, we measure company performance indirectly. In terms of The models shown in The dependent variable in A. The Determinants of Portfolio Company Survival The pseudo R 2 s in We find a significant increasing and at times concave relation between the lead investor's fund size and a portfolio company's survival from any of the first three rounds. This echoes the finding in the previous section that larger funds have higher exit rates. First-time funds that lead an investment round are associated with significantly worse survival probabilities from round 3. The more money the VC industry raised from investors at the time of the funding round, the less likely a portfolio company is to survive, and this is true across all three rounds. Interpreting fund inflows as a proxy for competition for deal flow, this suggests that funds make more marginal investment choices at times when investment capital is plentiful, leading to poorer survival records. A more favorable investment environment, as proxied by a lower average industry B/M ratio, significantly improves a company's chances of survival, again across all three rounds. The beneficial effect of low competition and favorable investment opportunities is strongest economically in the first two rounds. Surprisingly, more experienced VCs are associated with a 23 significantly lower survival probability. 27 Controlling for these factors, we find, in each of the fifteen probit models, that better networked investors are associated with significantly higher company survival probabilities. To illustrate the economic magnitude, consider a one-standard-deviation increase in the lead VC's eigenvector centrality measure. This increases the survival probability in the first round from the unconditional expectation of 66.8% to 72.4%, in the second round from 77.7% to 83.4%, and in the third round from 79.2% to 86.4%. As in the fund-level models, the network measures capturing the number and quality of relationships (degree and eigenvector) and access to other VCs' deal flow (indegree) have stronger economic effects on performance than do measures of future reciprocity (outdegree) and brokerage (betweenness). Using a sample of Canadian companies, Brander, Amit, and Antweiler We also re-estimate the models focusing only on rounds that were not syndicated. Here, we continue to find that portfolio companies benefit from receiving funding from well-networked VCs even if the investment itself was not syndicated. Thus, the influence a VC derives from having many syndication partners is useful even when the VC does not formally syndicate a given investment, which validates our choice of using syndication networks to proxy for the broader networks VCs operate in. B. Pooled Portfolio Company Survival Models So far, we have modeled round-by-round survival. We now take the panel nature of the data explicitly into account. We track each sample company from its first funding round across all rounds to the earlier of its exit or November 2003. The dependent variable equals one in round N if the company survived to round 27 This is based on using invested dollars to proxy for investment experience. Results are robust to using any of the other three experience proxies. 24 N+1. Unless it subsequently exited via an IPO or M&A transaction, the dependent variable is zero in the company's last recorded round. All models are estimated using panel probit estimators with random company effects. The panel is unbalanced since portfolio companies receive varying numbers of funding rounds. We estimate five models, including the five network measures one at a time. As before, network centrality is measured from the VC syndication network over the five-year window preceding the investment round. Note that the identity of the lead investor is allowed to change across rounds. The results are reported in Controlling for these factors, we find that a portfolio company's survival probability increases significantly, the better networked its lead investor. This is true for all five centrality measures. Except for betweenness, the economic effect in each case is large. A one-standard-deviation increase in the other four centrality measures is associated with a 6.6 to 8.2 percentage point increase from the unconditional survival probability of 66.8%, holding all other covariates at their sample means. C. Portfolio Company Exit Finally, we equate good performance with a successful exit (ignoring survival to another funding round) and ask whether the VC firm's network centrality helps accelerate a portfolio company's exit. that they may yet exit successfully after the end of our sample period). Allowing for right-censoring, the average time-to-exit in our sample is 24 quarters. 28 Econometrically, this is similar in spirit to Hellmann and Puri (2000) who investigate whether VC backing reduces the time it takes a start-up company to bring its product to market. 25 We relate the log time-to-exit to our network measures controlling for fund and firm characteristics, competition for deal flow and investment opportunities at the time of the company's first funding round, and conditions in the stock market in general and the IPO and M&A markets in particular. Market conditions are allowed to vary over time, to allow VC firms to react to improvements in (say) IPO conditions by taking a portfolio company public. We proxy for conditions in the stock market using the quarterly return on the NASDAQ Composite Index. To measure exit market conditions, we use the quarterly log number of IPOs and the quarterly log number of M&A deals in the portfolio company's Venture Economics industry. All three variables are lagged by a quarter, to allow for the necessary delay in preparing a company for exit. Our time-to-exit models are estimated in the form of accelerated-time-to-failure models. 29 These are hazard (or duration) models written with log time as the dependent variable. Parametric hazard models require that we specify a distribution for log time. While our results are robust to alternative choices, we assume that log time is normally distributed. This has the advantage that the hazard rate (the instantaneous probability of exiting in the next instance given that a company has not exited so far) first increases and then decreases over time. Other distributions imply either a constant hazard rate (e.g., exponential) or hazards that increase (or decrease) monotonically over time (e.g., Weibull or Gompertz). In the context of VC investments, monotonic hazard functions are implausible: It is neither the case that companies are never more likely to exit than at the time of their first round (a monotonically decreasing hazard function) nor that companies become ever more likely to exit the longer they have languished in the VC's portfolio (a monotonically increasing hazard function). 30 The results are reported in Controlling for these effects, we find that each of the five centrality measures has a negative and significant effect on time-to-exit. Eigenvector has the largest effect economically. A one-standard-deviation increase in the lead VC's eigenvector centrality is associated with a two-quarter decrease from the unconditional time-to-exit of 24 quarters. The corresponding effects for the three degree network measures are around one quarter. Thus, companies benefit from being backed by VCs who have many ties (degree), especially when these ties involve other well-connected VCs (eigenvector). V. Further Robustness Tests A. Robustness to Alternative Explanations We now investigate an alternative hypothesis for the positive relation between exits and network centrality found in Sections III and IV. Better networked VCs may be able to take more marginal companies public, thus generating the appearance of better performance as measured by the VC's exit rate or a portfolio company's survival probability, but which would presumably not be reflected in actual investment returns (which we do not observe). To test this alternative hypothesis, we focus on two quality indicators: Whether the portfolio company had positive net earnings when it went public, and whether it survived the first three years of trading on the public markets. We gather data on earnings for the last 12 month (LTM) period before the IPO from Compustat 31 and supplement these data with LTM earnings from Thomson Financial's SDC IPO database as well as hard copies of IPO prospectuses where necessary. We then sort all 16,315 portfolio companies that received their first institutional round of funding from a sample VC fund between 1980 and 1999 into quartiles 31 Compustat backfills data when companies go public. 27 based on the network centrality of their lead first-round VC. Contrary to the alternative hypothesis, the best networked VCs take companies public that are less likely to have negative earnings at the time of the IPO. For instance, 51% of companies in the highest quartile by degree have negative pre-IPO earnings vs. nearly two-thirds of companies in the lowest quartile. This suggests that being well-networked either helps the VC select more promising companies to begin with, or allows the VC to add more value to the start-up resulting in a higher-quality company by the time of the IPO. Either of these interpretations is consistent with the motivation for our study. Next, we estimate the probability that a company has negative earnings at the time of the IPO, as a function of fund characteristics, proxies for competition for deal flow and investment opportunities, fund experience, and our measures of how well networked each fund's parent firm is. We find no significant relation between four of the five network centrality measures and the probability of having negative earnings at the time of the IPO (not reported). 32 To investigate post-IPO survival, we code a company as delisting involuntarily if CRSP has assigned it a delisting code in the 400s or 500s and the delisting date occurs on or before the third anniversary of the IPO. 33 Of the 2,527 sample companies that go public by November 2003, 7% are delisted involuntarily. 34 We again sort the sample into quartiles by the lead VC's network centrality and find a positive relation between firm quality and the lead VC's network centrality, contrary to what we would expect under the alternative hypothesis. For instance, 4.9% of companies backed by the VCs with the highest outdegree are delisted involuntarily within three years of going public vs. 10.5% of companies backed by the worstnetworked VCs. When we estimate probit models of the likelihood that a firm delists involuntarily within three years of going public (as a function of fund characteristics, proxies for competition for deal flow and investment opportunities, fund experience, and our measures of how well networked each fund's parent firm is), we also find no support for the alternative hypothesis. The only variables predicting delisting are the proxy for 32 The exception is indegree which has a positive and significant coefficient. We interpret this as providing at best weak support for the alternative hypothesis. 33 Following standard practice, mergers and exchange offers are not classified as involuntary delisting events. 34 Note that as we do not have a full three-year window for very recent IPOs, it is conceivable that this understates the delisting rate somewhat. On the other hand, there were extremely few VC-backed IPOs in 2001-2003. 28 competition for deal flow and the lead VC's investment experience: Companies funded at times when more money was raised by the VC industry have a significantly higher delisting probability, 35 while companies backed by more experienced VCs have a significantly lower delisting probability. In conclusion, better-networked VCs do not appear to be associated with lower-quality IPO exits (as measured by earnings at the time of the IPO and subsequent survival). B. Location-and Industry-specific Networks The network measures we have used thus far implicitly assume that each VC in the U.S. potentially has ties to every other VC in the U.S. To the extent that VC networks in truth are more geographically concentrated, or involve only VCs specializing in a certain industry, we may underestimate a VC's network centrality. For instance, a given biotech VC firm may be central in a network of biotech VCs, but may lack connections to non-biotech VCs in the overall network of U.S.-based VCs. Similarly, a VC firm headquartered in Silicon Valley may be well connected in California but not in a network that includes East Coast VC firms. To assess the robustness of our findings we have re-estimated all our models using centrality measures derived from (a) industry-specific networks defined using the six broad Venture Economics industries, and (b) a network of Californian VC firms. (We refrain from constructing networks for other geographic areas due to the comparatively small number of VC firms in areas outside California.) In each case, we continue to construct the networks on the basis of trailing five-year windows. To conserve space, we do not report the results in tables. Using industry-specific networks slightly strengthens our fund-level results, in the sense of both higher adjusted R 2 s and larger economic effects. For instance, a one-standard-deviation increase in a firm's indegree increases its funds' exit rates by 2.5 percentage points in the industry-specific models, compared to 2.2 percentage points using the overall network. In the company-level models, our results are qualitatively unchanged compared to Tables VII through IX, and the industry network measures do not obviously dominate the overall network measures. Restricting the network to Californian VCs reduces the sample of funds to 872 funds (for which all 35 This is consistent with the "money chasing deals" phenomenon of Gompers and Lerner (2000) resulting in more marginal companies being funded by the VC industry. 29 necessary variables are available) and the sample of portfolio companies to 4,691. The network measures continue to improve fund performance significantly, and the economic magnitude of the effects is considerably larger than before: On the order of 4-5 percentage point improvements in fund exit rates (from the unconditional mean of 35.7%), compared to around two percentage points in the overall sample. In the company-level models, our network measures continue to be positively and significantly related to company survival and exit probabilities, and the economic magnitude of the effects is similar to the models shown in Tables VII through IX. VI. How do VC Firms Become Networked? Our results so far suggest that VC firms that occupy more central, or influential, positions in the VC network enjoy better investment performance, both at the fund and the portfolio company level. But how do VC firms become networked in the first place? It seems likely that an emerging track record of successful investing makes a VC firm a more desirable syndication partner in the future, which in turn will improve its network position over time. Such a track record might be built around successful portfolio exits, particularly eye-catching IPOs, or -according to conversations we have had with venture capitaliststhe ability to persuade unrelated VCs to lead a follow-on funding round for a portfolio company. To explore the evolution of a first-time VC firm's network position empirically, we model its network centrality in year t (using each of the five centrality measures as the dependent variable) as a function of the log number of portfolio companies that it exited via an IPO or an M&A transaction in year t-1; the log number of portfolio companies that received follow-on funding in year t-1 in a round led by an outside VC (defined as a VC firm that was not already an investor in the portfolio company); and its accumulated investment experience in year t-1 (using the log aggregate dollar amount it has invested since inception). 36 To control for how "eye-catching" its IPOs were, we also include the average degree of underpricing of its prior-year IPOs. Finally, we control for the fact that a VC firm's network position may naturally slip as the network grows in size, by including the log number of new funds raised during the year. 36 Our results are robust to using longer lags, though we lose observations. 30 We expect persistence in a VC firm's network position, in part because economically, relationships take time to establish but once they are, they likely endure over time; and in part due to the way we construct the network measures. Therefore, we estimate dynamic panel data models under the assumption that the errors follow an AR(1) process. To control for unobserved heterogeneity in firm characteristics, such as skill or personal contacts, we include firm fixed effects, and we allow for unbalanced panels to capture the fact that some VC firms are in the sample for longer than others. The resulting estimator is due to Baltagi and Wu (1999). The results are reported in columns The models have high pseudo-R 2 s, ranging from 17.6% for the betweenness model to 28.7% for the indegree model. Auto-correlation is around 83%, consistent with persistence in network position. The firm fixed effects are significant throughout, suggesting that there is VC firm-specific heterogeneity omitted from the specification. Likely candidates are investment skill and personal network contacts VCs may have acquired through prior employment at an established VC firm. Across all five models, first-time funds improve their network positions as they become more experienced through time. Growth in the size of the network generally has no effect on centrality, though a VC firm's eigenvector centrality actually improves as more new funds enter the industry. Controlling for these factors, we find that a VC firm's network position is unrelated to the number of portfolio companies it has exited through an IPO or M&A transaction, with one exception: In the case of outdegree, we find a statistically weak relation to the lagged number of IPOs and a stronger relation to the lagged number of M&A deals. One plausible interpretation for this finding is that a VC firm has to prove its ability to find and produce winners before many other VCs will accept invitations into its syndicates. Refinancings lead-managed by outside VC, on the other hand, have the conjectured positive and significant effect on a VC firm's future network position in all five models. The evidence on how eye-catching the VC firm's prior-year IPOs were varies in magnitude and significance across the five models. For indegree, degree, and eigenvector, higher underpricing is associated with subsequent improvement in the VC firm's network position. When we use other plausible 31 proxies for eye-catching IPOs (such as the average first-day market capitalization of the VC firm's IPOs, to capture "home runs"), we find no relation to network position (results not shown). The same is true when we attempt to make allowance for the quality (rather than quantity) of a VC firm's exits using the quality measures explored in Section V.A (such as the fraction of IPOs with negative earnings at the time of the IPO or that were delisted within three years, lagged appropriately) and the average three-year post-IPO buy-and-hold abnormal return of the firm's IPOs. Finally, we investigate the dynamic relation between outdegree and indegree. In Section III, we argued that outdegree may have a relatively smaller economic effect on fund performance than the other network measures because it captures a VC firm's investment in future reciprocity, which takes some time to pay off. The dynamic models in VII. Conclusions Many financial markets are characterized by strong relationships and networks, rather than arm'slength, spot-market transactions. We examine the performance consequences of this organizational choice in the context of relationships established when VCs syndicate portfolio company investments. We use a comprehensive sample of U.S. based VCs over the period 1980 to 2003. To the best of our knowledge, this is the first study to examine the relation between fund and portfolio company performance and measures of networking among VCs. Controlling for known determinants of VC investment performance, we find that VC funds whose parent firms enjoy more influential network positions have significantly better performance, as measured by the proportion of portfolio investments that are successfully exited through an initial public offering or a sale to another company. Similarly, the portfolio companies of better networked VC firms are significantly 32 more likely to survive to subsequent rounds of financing and to eventual exit. The magnitude of these effects is economically large, and is robust to a wide range of specifications. Economically, VC firms benefit the most from having a wide range of relationships, especially if these involve other well-networked VC firms, and from having access to other VCs' deal flow. One way to gain access to deal flow is for a VC firm to invite other VCs into its syndicates today, which over time appears to lead to reciprocal co-investment opportunities. The network measure with the least economic significance is betweenness, which captures a VC firm's ability to act as a broker between other VCs. This suggests that indirect relationships (those requiring intermediation) play a lesser role in the venture capital market. Interestingly, once we control for network effects, the importance of how much investment experience a VC has is reduced, and in some specifications, eliminated. Our analysis provides a first look at the economic importance of networks as a choice of organizational form in the venture capital industry. We leave for future research the question how networking affects performance in other financial markets, such as syndicated lending, bond or equity underwriting, and investment bank-institutional investor relationships. If more highly networked VCs enjoy better investment performance, our findings have ramifications for institutional investors choosing which VC fund to invest in. Additionally, our analysis provides a deeper understanding of the possible drivers of cross-sectional performance of VC funds. Our findings also shed light on the industrial organization of the VC market. Given the large returns to being well-networked we document, enhancing one's network position should be an important strategic consideration for an incumbent VC, while presenting a potential barrier to entry for new VCs. Here, row vectors record syndicate leadership while column vectors record syndicate membership, and the matrix is no longer symmetric. The row vectors show that A has led (at least) one syndicate in which C was a member, B has led at least one syndicate in which A was a member, C has led one syndicate each in which A, B and D were members, and D has led no syndicates. The column vectors show that A has been a (non-lead) member of syndicates led by B and C, B has been a (non-lead) member of syndicate(s) led by C, C has been a (non-lead) member of syndicate(s) led by A, and D has been a (non-lead) member of syndicate(s) led by C. Intuitively, C appears the best connected: C leads more syndicates than the other VCs, participates in more syndicates than any VC except A (with whom C ties), and is the only VC to have syndicated with D. Thus, C is said to have greater "centrality," in the sense of having a highly favored position in the network giving access to information, deal flow, deeper pools of capital, contacts, expertise, and so on. C's only apparent shortcoming (in this network) is the fact that it is not often (invited to be) present in syndicates led by the other VCs. The five centrality measures used in our study are calculated from the two adjacency matrices, and are summarized for the four VCs in the following

How does the Web look? How could we tell an abnormal social network from a normal one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks to sociology to biology and many more. Indeed, any M: N relation in database terminology can be represented as a graph. A lot of these questions boil down to the following: “How can we generate synthetic but realistic graphs? ” To answer this, we must first understand what patterns are common in real-world graphs and can thus be considered a mark of normality/realism. This survey give an overview of the incredible variety of work that has been done on these problems. One of our main contributions is the integration of points of view from physics, mathematics, sociology, and computer science. Further, we briefly describe recent advances on some related and interesting graph problems.

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