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.

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of large sizes of these networks, the distances between most their vertices are short — a feature known as the “smallworld” effect. We discuss how growing networks self-organize into scale-free structures and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in Nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems

Abstract. The so-called "Web of Trust " is one of the ultimate goals of the Semantic Web. Research on the topic of trust in this domain has focused largely on digital signatures, certificates, and authentication. At the same time, there is a wealth of research into trust and social networks in the physical world. In this paper, we describe an approach for integrating the two to build a web of trust in a more social respect. This paper describes the applicability of social network analysis to the semantic web, particularly discussing the multi-dimensional networks that evolve from ontological trust specifications. As a demonstration of algorithms used to infer trust relationships, we present several tools that allow users to take advantage of trust metrics that use the network. 1

This paper introduces the newscast model of computation for large-scale computing on the Internet. The engine realizing this model is a lazy fully distributed information propagation protocol among the participants which is responsible for membership management and communication. It maintains a constantly changing communication graph over the participants. This graph has useful emergent properties like small diameter and sufficiently random structure without deploying special purpose protocols to achieve these properties. For adding a new participant only the address of an arbitrary member is needed and for removal no action is necessary. We provide theoretical and empirical evidence that besides being simple and lightweight our newscast computing engine is extremely scalable and robust. We also suggest some interesting application areas including information dissemination, monitoring of large systems, resource sharing and efficient multicasting.

In this paper we present analytical techniques that can be used to better understand the behavior of malware, a generic term that refers to all kinds of malicious software programs propagating on the Internet, such as e-mail viruses and worms. We develop a modeling methodology based on Interactive Markov Chains that is able to capture many aspects of the problem, especially the impact of the underlying topology on the spreading characteristics of malware. We propose numerical methods to obtain useful bounds and approximations in the case of very large systems, validating our results through simulation. An analytic methodology represents a fundamentally important step in the development of effective countermeasures for future malware activity. Furthermore, we believe our approach can help to understand a wide range of "dynamic interactions on networks ", such as routing protocols and peer-to-peer applications. I.

While most research on the topic of trust on the semantic web has focused largely on digital signatures, certificates, and authentication, more social notions of trust which are reputation-based are starting to gain attention. In this paper, we describe an algorithm for generating locally-calculated reputation ratings from a Semantic Web Social Network. We present mathematical and experimental results that show the effectiveness of this algorithm to accurately infer the reputation of a node. We then describe TrustMail, an application that uses the network for rating email.

In this paper we present an experimental study of the properties of web graphs. We study a large crawl from 2001 of 200M pages and about 1.4 billion edges made available by the WebBase project at Stanford [17]. We report our experimental findings on the topological properties of such graphs, such as the number of bipartite cores and the distribution of degree, PageRank values and strongly connected components.

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The so-called "Web of Trust " is one of the ultimate goals of the Semantic Web. Research on the topic of trust in this domain has focused largely on digital signatures, certificates, and authentication. More social notions of trust which are reputation based are beginning to gain some attention in their own right, but have been traditionally overlooked. In this paper, we describe an algorithm for generating locallycalculated reputation ratings from a semantic network. We present mathematical and experimental results that show the effectiveness of this algorithm to accurately infer the reputation of a node. We then describe TrustMail, an application that uses the network for rating relevant emails

In this article the different features exhibited by four types of natural and artificial networks are reviewed, after a brief account of the basic quantitative characterizations that allow to measure network complexity. Some key questions that will be explored are: 1. What mechanisms have originated observed topological regularities in complex networks? 2. To what extent does optimization shape network topology ? 3. What is the origin of homeostasis in complex networks? 4. Is homeostasis a driving force or a side effect in network topology? 5. Is tinkering an inevitable component of network evolution ? 6. Are engineered systems free of tinkering? Comparison between the mechanisms that drive the building process of different graphs reveals that optimization might be a driving force, canalized in biological systems by both tinkering and the presence of conflicting constraints common to any hard multidimensional optimization process. Conversely, the presence of global features in technology graphs that closely resemble those observed in biological webs indicates that, in spite of the engineered design that should lead to hierarchical structures (such as the one shown in Figure 1) the tinkerer seems to be at work. 2. MEASURING NETWORK COMPLEXITY Since we are interested in comparing the global features of both biological and artificial (engineered) networks, we need to consider a number of quantitative measures in order to characterize them properly. In order to do so, the network structure is represented by a graph #, as before. Some of these measures (minimal distance, clustering coefficient) are usually applied to topological (i.e., static) descriptors of the graph structure, but others (entropy, redundancy, degeneracy) also apply to states that average dynamic variables