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419
Relevance of Massively Distributed Explorations of the Internet Topology: Simulation Results
, 2005
"... Internet maps are generally constructed using the traceroute tool from a few sources to many destinations. It appeared recently that this exploration process gives a partial and biased view of the real topology, which leads to the idea of increasing the number of sources to improve the quality of ..."
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Cited by 42 (14 self)
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Internet maps are generally constructed using the traceroute tool from a few sources to many destinations. It appeared recently that this exploration process gives a partial and biased view of the real topology, which leads to the idea of increasing the number of sources to improve the quality of the maps. In this paper, we present a set of experiments we have conduced to evaluate the relevance of this approach. It appears that the statistical properties of the underlying network have a strong influence on the quality of the obtained maps, which can be improved using massively distributed explorations. Conversely, we show that the exploration process induces some properties on the maps. We validate our analysis using realworld data and experiments and we discuss its implications.
Information Theory of Complex Networks: on evolution and architectural constraints
 In
, 2004
"... Complex networks are characterized by highly heterogeneous distributions of links, often pervading the presence of key properties such as robustness under node removal. Several correlation measures have been defined in order to characterize the structure of these nets. Here we show that mutual infor ..."
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Cited by 42 (1 self)
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Complex networks are characterized by highly heterogeneous distributions of links, often pervading the presence of key properties such as robustness under node removal. Several correlation measures have been defined in order to characterize the structure of these nets. Here we show that mutual information, noise and joint entropies can be properly defined on a static graph. These measures are computed for a number of real networks and analytically estimated for some simple standard models. It is shown that real networks are clustered in a welldefined domain of the entropy/noise space. By using simulated annealing optimization, it is shown that optimally heterogeneous nets actually cluster around the same narrow domain, suggesting that strong constraints actually operate on the possible universe of complex networks. The evolutionary implications are discussed.
Epidemic spreading in complex networks with degree correlations.
 In Statistical mechanics of complex networks
, 2003
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Error and Attack Tolerance of Complex Networks
, 2004
"... Communication/transportation systems are often subjected to failures and attacks. Here we represent such systems as networks and we study their ability to resist failures (attacks) simulated as the breakdown of a group of nodes of the networkchosen at random (chosen accordingly to degree or load). W ..."
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Cited by 36 (1 self)
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Communication/transportation systems are often subjected to failures and attacks. Here we represent such systems as networks and we study their ability to resist failures (attacks) simulated as the breakdown of a group of nodes of the networkchosen at random (chosen accordingly to degree or load). We consider and compare the results for two di#erent networktopologies: the Erd#osR#enyi random graph and the Barab#asiAlbert scalefree network. We also discuss brie#y a dynamical model recently proposed to take into account the dynamical redistribution of loads after the initial damage of asi)4 node of the network.
Proximity Tracking on TimeEvolving Bipartite Graphs
"... Given an authorconference network that evolves over time, which are the conferences that a given author is most closely related with, and how do they change over time? Large timeevolving bipartite graphs appear in many settings, such as social networks, cocitations, marketbasket analysis, and co ..."
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Cited by 35 (5 self)
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Given an authorconference network that evolves over time, which are the conferences that a given author is most closely related with, and how do they change over time? Large timeevolving bipartite graphs appear in many settings, such as social networks, cocitations, marketbasket analysis, and collaborative filtering. Our goal is to monitor (i) the centrality of an individual node (e.g., who are the most important authors?); and (ii) the proximity of two nodes or sets of nodes (e.g., who are the most important authors with respect to a particular conference?) Moreover, we want to do this efficiently and incrementally, and to provide “anytime ” answers. We propose pTrack and cTrack, which are based on random walk with restart, and use powerful matrix tools. Experiments on real data show that our methods are effective and efficient: the mining results agree with intuition; and we achieve up to 15∼176 times speedup, without any quality loss. 1
Network Science
 In Annual Review of Information Science & Technology
, 2007
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Information spreading in stationary markovian evolving graphs
 In Proc. of the 23rd IEEE International Parallel and Distributed Processing Symposium (IPDPS
, 2009
"... Markovian evolving graphs [2] are dynamicgraph models where the links among a fixed set of nodes change during time according to an arbitrary Markovian rule. They are extremely general and they can well describe important dynamicnetwork scenarios. We study the speed of information spreading in the ..."
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Cited by 34 (9 self)
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Markovian evolving graphs [2] are dynamicgraph models where the links among a fixed set of nodes change during time according to an arbitrary Markovian rule. They are extremely general and they can well describe important dynamicnetwork scenarios. We study the speed of information spreading in the stationary phase by analyzing the completion time of the flooding mechanism. We prove a general theorem that establishes an upper bound on flooding time in any stationary Markovian evolving graph in terms of its nodeexpansion properties. We apply our theorem in two natural and relevant cases of such dynamic graphs: edgeMarkovian evolving graphs [24, 7] where the probability of existence of any edge at time t depends on the existence (or not) of the same edge at time t − 1; geometric Markovian evolving graphs [4, 10, 9] where the Markovian behaviour is yielded by n mobile radio stations, with fixed transmission radius, that perform n independent random walks over a square region of the plane. In both cases, the obtained upper bounds are shown to be nearly tight and, in fact, they turn out to be tight for a large range of the values of the input parameters. 1
Dynamics of Large Networks
, 2008
"... A basic premise behind the study of large networks is that interaction leads to complex collective behavior. In our work we found very interesting and counterintuitive patterns for time evolving networks, which change some of the basic assumptions that were made in the past. We then develop models ..."
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Cited by 33 (0 self)
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A basic premise behind the study of large networks is that interaction leads to complex collective behavior. In our work we found very interesting and counterintuitive patterns for time evolving networks, which change some of the basic assumptions that were made in the past. We then develop models that explain processes which govern the network evolution, fit such models to real networks, and use them to generate realistic graphs or give formal explanations about their properties. In addition, our work has a wide range of applications: it can help us spot anomalous graphs and outliers, forecast future graph structure and run simulations of network evolution. Another important aspect of our research is the study of “local ” patterns and structures of propagation in networks. We aim to identify building blocks of the networks and find the patterns of influence that these blocks have on information or virus propagation over the network. Our recent work included the study of the spread of influence in a large persontoperson
Mixing patterns and community structure in networks
 in Statistical Mechanics of Complex Networks
"... Common experience suggests that many networks might possess community structure—division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects structure of this kind. We apply the algorithm to a number of realw ..."
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Cited by 30 (1 self)
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Common experience suggests that many networks might possess community structure—division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects structure of this kind. We apply the algorithm to a number of realworld networks and show that they do indeed possess nontrivial community structure. We suggest a possible explanation for this structure in the mechanism of assortative mixing, which is the preferential association of network vertices with others that are like them in some way. We show by simulation that this mechanism can indeed account for community structure. We also look in detail at one particular example of assortative mixing, namely mixing by vertex degree, in which vertices with similar degree prefer to be connected to one another. We propose a measure for mixing of this type which we apply to a variety of networks, and also discuss the implications for network structure and the formation of a giant component in assortatively mixed networks. 1
Colibri: Fast Mining of Large Static and Dynamic Graphs
"... Lowrank approximations of the adjacency matrix of a graph are essential in finding patterns (such as communities) and detecting anomalies. Additionally, it is desirable to track the lowrank structure as the graph evolves over time, efficiently and within limited storage. Real graphs typically have ..."
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Cited by 30 (7 self)
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Lowrank approximations of the adjacency matrix of a graph are essential in finding patterns (such as communities) and detecting anomalies. Additionally, it is desirable to track the lowrank structure as the graph evolves over time, efficiently and within limited storage. Real graphs typically have thousands or millions of nodes, but are usually very sparse. However, standard decompositions such as SVD do not preserve sparsity. This has led to the development of methods such as CUR and CMD, which seek a nonorthogonal basis by sampling the columns and/or rows of the sparse matrix. However, these approaches will typically produce overcomplete bases, which wastes both space and time. In this paper we propose the family of Colibri methods to deal with these challenges. Our version for static graphs, ColibriS, iteratively finds a nonredundant basis and we prove that it has no loss of accuracy compared to the best competitors (CUR and CMD), while achieving significant savings in space and time: on real data, ColibriS requires much less space and is orders of magnitude faster (in proportion to the square of the number of nonredundant columns). Additionally, we propose an efficient update algorithm for dynamic, timeevolving graphs, ColibriD. Our evaluation on a large, real network traffic dataset shows that ColibriD is over 100 times faster than the best published competitor (CMD).