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60
The structure and function of complex networks
 SIAM REVIEW
, 2003
"... 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, ..."
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Cited by 1407 (9 self)
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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 smallworld effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
Evolution of networks
 Adv. Phys
, 2002
"... 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 rece ..."
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Cited by 268 (2 self)
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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 scalefree 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 selforganize into scalefree 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
Models of the small world
 J. Stat. Phys
, 2000
"... It is believed that almost any pair of people in the world can be connected to one another by a short chain of intermediate acquaintances, of typical length about six. This phenomenon, colloquially referred to as the ``six degrees of separation,' ' has been the subject of considerable recent interes ..."
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Cited by 85 (2 self)
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It is believed that almost any pair of people in the world can be connected to one another by a short chain of intermediate acquaintances, of typical length about six. This phenomenon, colloquially referred to as the ``six degrees of separation,' ' has been the subject of considerable recent interest within the physics community. This paper provides a short review of the topic. KEY WORDS: social networks. Small world; networks; disordered systems; graph theory;
Meanfield solution of the smallworld network model
, 2000
"... The smallworld network model is a simple model of the structure of social networks, which simultaneously possesses characteristics of both regular lattices and random graphs. The model consists of a onedimensional lattice with a low density of shortcuts added between randomly selected pairs of poi ..."
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Cited by 62 (6 self)
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The smallworld network model is a simple model of the structure of social networks, which simultaneously possesses characteristics of both regular lattices and random graphs. The model consists of a onedimensional lattice with a low density of shortcuts added between randomly selected pairs of points. These shortcuts greatly reduce the typical path length between any two points on the lattice. We present a meanfield solution for the average path length and for the distribution of path lengths in the model. This solution is exact in the limit of large system size and either large or small number of shortcuts. 1 Social networks, such as networks of friends, have two characteristics which one might imagine were contradictory. First, they show “clustering, ” meaning that two of your friends are far more likely also to be friends of one another than two people chosen from the population at random. Second, they exhibit what has become known as the “smallworld effect,” namely that any two people can establish contact by going through only a short chain of
Evolutionary games on graphs
, 2007
"... Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to ..."
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Cited by 54 (0 self)
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Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in nonequilibrium statistical physics. This review gives a tutorialtype overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by nonmeanfieldtype social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner’s Dilemma, the Rock–Scissors–Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
Models of the Small World  A Review
"... It is believed that almost any pair of people in the world can be connected to one another by a short chain of intermediate acquaintances, of typical length about six. This phenomenon, colloquially referred to as the "six degrees of separation," has been the subject of considerable recent interest w ..."
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Cited by 34 (0 self)
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It is believed that almost any pair of people in the world can be connected to one another by a short chain of intermediate acquaintances, of typical length about six. This phenomenon, colloquially referred to as the "six degrees of separation," has been the subject of considerable recent interest within the physics community. This paper provides a short review of the topic.
Exact Solution of Site and Bond Percolation on SmallWorld Networks
, 2000
"... We study percolation on smallworld networks, which has been proposed as a simple model of the propagation of disease. The occupation probabilities of sites and bonds correspond to the susceptibility of individuals to the disease and the transmissibility of the disease respectively. We give an ex ..."
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Cited by 27 (3 self)
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We study percolation on smallworld networks, which has been proposed as a simple model of the propagation of disease. The occupation probabilities of sites and bonds correspond to the susceptibility of individuals to the disease and the transmissibility of the disease respectively. We give an exact solution of the model for both site and bond percolation, including the position of the percolation transition at which epidemic behavior sets in, the values of the two critical exponents governing this transition, and the mean and variance of the distribution of cluster sizes (disease outbreaks) below the transition. 1 In the late 1960s, Milgram performed a number of experiments which led him to conclude that, despite there being several billion human beings in the world, any two of them could be connected by only a short chain of intermediate acquaintances of typical length about six [1]. This result, known as the "smallworld e#ect", has been confirmed by subsequent studies and ...
Biological network comparison using graphlet degree distribution
 Bioinformatics
"... Motivation: Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally infeasible, and thus heuristics, such as the degr ..."
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Cited by 26 (1 self)
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Motivation: Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally infeasible, and thus heuristics, such as the degree distribution, clustering coefficient, diameter, and relative graphlet frequency distribution have been sought. It is easy to demonstrate that two networks are different by simply showing a short list of properties in which they differ. It is much harder to show that two networks are similar, as it requires demonstrating their similarity in all of their exponentially many properties. Clearly, it is computationally prohibitive to analyze all network properties, but the larger the number of constraints we impose in determining network similarity, the more likely it
"It’s a small world after all": NoC performance optimization via longrange link insertion
 IEEE TRANS. VERY LARGE SCALE INTEGRATION SYSTEMS
, 2006
"... Networksonchip (NoCs) represent a promising solution to complex onchip communication problems. The NoC communication architectures considered so far are based on either completely regular or fully customized topologies. In this paper, we present a methodology to automatically synthesize an archi ..."
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Cited by 24 (5 self)
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Networksonchip (NoCs) represent a promising solution to complex onchip communication problems. The NoC communication architectures considered so far are based on either completely regular or fully customized topologies. In this paper, we present a methodology to automatically synthesize an architecture which is neither regular nor fully customized. Instead, the communication architecture we propose is a superposition of a few longrange links and a standard mesh network. The few applicationspecific longrange links we insert significantly increase the critical traffic workload at which the network transitions from a free to a congested state. This way, we can exploit the benefits offered by both complete regularity and partial topology customization. Indeed, our experimental results demonstrate a significant reduction in the average packet latency and a major improvement in the achievable network through with minimal impact on network topology.
Small and other worlds: Global network structures from local processes
 American Journal of Sociology
, 2005
"... Using simulation, we contrast global network structures—in particular, small world properties—with the local patterning that generates the network. We show how to simulate Markov graph distributions based on assumptions about simple local social processes. We examine the resulting global structures ..."
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Cited by 18 (1 self)
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Using simulation, we contrast global network structures—in particular, small world properties—with the local patterning that generates the network. We show how to simulate Markov graph distributions based on assumptions about simple local social processes. We examine the resulting global structures against appropriate Bernoulli graph distributions and provide examples of stochastic global “worlds, ” including small worlds, long path worlds, and nonclustered worlds with many fourcycles. In light of these results we suggest a locally specified social process that produces small world properties. In examining movement from structure to randomness, parameter scaling produces a phase transition at a “temperature ” where regular structures “melt ” into stochastically based counterparts. We provide examples of “frozen ” structures, including “caveman ” graphs, bipartite structures, and cyclic structures.