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Statistical mechanics of complex networks
 Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
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Cited by 1244 (8 self)
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Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 231 (0 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such
A Survey of Models of Network Formation: Stability and Efficiency
, 2003
"... I survey the recent literature on the formation of networks. I provide definitions of network games, a number of examples of models from the literature, and discuss some of what is known about the (in)compatibility of overall societal welfare with individual incentives to form and sever links. ..."
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Cited by 200 (14 self)
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I survey the recent literature on the formation of networks. I provide definitions of network games, a number of examples of models from the literature, and discuss some of what is known about the (in)compatibility of overall societal welfare with individual incentives to form and sever links.
Complex networks: Structure and dynamics
, 2006
"... Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly interconnected dynamical units. The first approach to capture the global properties of such systems is to ..."
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Cited by 196 (5 self)
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Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly interconnected dynamical units. The first approach to capture the global properties of such systems is to model them as graphs whose nodes represent the dynamical units, and whose links stand for the interactions between them. On the one hand, scientists have to cope with structural issues, such as characterizing the topology of a complex wiring architecture, revealing the unifying principles that are at the basis of real networks, and developing models to mimic the growth of a network and reproduce its structural properties. On the other hand, many relevant questions arise when studying complex networks ’ dynamics, such as learning how a large ensemble of dynamical systems that interact through a complex wiring topology can behave collectively. We review the major concepts and results recently achieved in the study of the structure and dynamics of complex networks, and summarize the relevant applications of these ideas in many different disciplines,
Gossipbased aggregation in large dynamic networks
 ACM Trans. Comput. Syst
, 2005
"... As computer networks increase in size, become more heterogeneous and span greater geographic distances, applications must be designed to cope with the very large scale, poor reliability, and often, with the extreme dynamism of the underlying network. Aggregation is a key functional building block fo ..."
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Cited by 189 (36 self)
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As computer networks increase in size, become more heterogeneous and span greater geographic distances, applications must be designed to cope with the very large scale, poor reliability, and often, with the extreme dynamism of the underlying network. Aggregation is a key functional building block for such applications: it refers to a set of functions that provide components of a distributed system access to global information including network size, average load, average uptime, location and description of hotspots, and so on. Local access to global information is often very useful, if not indispensable for building applications that are robust and adaptive. For example, in an industrial control application, some aggregate value reaching a threshold may trigger the execution of certain actions; a distributed storage system will want to know the total available free space; loadbalancing protocols may benefit from knowing the target average load so as to minimize the load they transfer. We propose a gossipbased protocol for computing aggregate values over network components in a fully decentralized fashion. The class of aggregate functions we can compute is very broad and includes many useful special cases such as counting, averages, sums, products, and extremal values. The protocol is suitable for extremely large and highly dynamic systems due to its proactive structure—all nodes receive the aggregate value continuously, thus being able to track
Computing and Applying Trust in Webbased Social Networks
, 2005
"... The proliferation of webbased social networks has lead to new innovations in social networking, particularly by allowing users to describe their relationships beyond a basic connection. In this dissertation, I look specifically at trust in webbased social networks, how it can be computed, and how ..."
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Cited by 137 (15 self)
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The proliferation of webbased social networks has lead to new innovations in social networking, particularly by allowing users to describe their relationships beyond a basic connection. In this dissertation, I look specifically at trust in webbased social networks, how it can be computed, and how it can be used in applications. I begin with a definition of trust and a description of several properties that affect how it is used in algorithms. This is complemented by a survey of webbased social networks to gain an understanding of their scope, the types of relationship information available, and the current state of trust. The computational problem of trust is to determine how much one person in the network should trust another person to whom they are not connected. I present two sets of algorithms for calculating these trust inferences: one for networks with binary trust ratings, and one for continuous ratings. For each rating scheme, the algorithms are built upon the defined notions of trust. Each is then analyzed theoretically and with respect to simulated and actual trust networks to determine how accurately they calculate the opinions of people in the system. I show that in both rating schemes the algorithms
The LargeScale Structure of Semantic Networks: Statistical Analyses and a Model of Semantic Growth
 Cognitive Science
"... We present statistical analyses of the largescale structure of three types of semantic networks: word associations, WordNet, and Roget's thesaurus. We show that they have a smallworld structure, characterized by sparse connectivity, short average pathlengths between words, and strong local ..."
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Cited by 123 (1 self)
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We present statistical analyses of the largescale structure of three types of semantic networks: word associations, WordNet, and Roget's thesaurus. We show that they have a smallworld structure, characterized by sparse connectivity, short average pathlengths between words, and strong local clustering. In addition, the distributions of the number of connections follow power laws that indicate a scalefree pattern of connectivity, with most nodes having relatively few connections joined together through a small number of hubs with many connections. These regularities have also been found in certain other complex natural networks, such as the world wide web, but they are not consistent with many conventional models of semantic organization, based on inheritance hierarchies, arbitrarily structured networks, or highdimensional vector spaces. We propose that these structures reflect the mechanisms by which semantic networks grow. We describe a simple model for semantic growth, in which each new word or concept is connected to an existing network by differentiating the connectivity pattern of an existing node. This model generates appropriate smallworld statistics and powerlaw connectivity distributions, and also suggests one possible mechanistic basis for the effects of learning history variables (ageofacquisition, usage frequency) on behavioral performance in semantic processing tasks.
Networks, Dynamics, and the SmallWorld Phenomenon
 American Journal of Sociology
, 1999
"... The smallworld phenomenon formalized in this article as the coincidence of high local clustering and short global separation, is shown to be a general feature of sparse, decentralized networks that are neither completely ordered nor completely random. Networks of this kind have received little atte ..."
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Cited by 114 (1 self)
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The smallworld phenomenon formalized in this article as the coincidence of high local clustering and short global separation, is shown to be a general feature of sparse, decentralized networks that are neither completely ordered nor completely random. Networks of this kind have received little attention, yet they appear to be widespread in the social and natural sciences, as is indicated here by three distinct examples. Furthermore, small admixtures of randomness to an otherwise ordered network can have a dramatic impact on its dynamical, as well as structural, properties—a feature illustrated by a simple model of disease transmission.
Characterization of complex networks: A survey of measurements
 ADVANCES IN PHYSICS
, 2005
"... Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics and function of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of mea ..."
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Cited by 94 (7 self)
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Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics and function of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements organized into classes. Special attention is given to relating complex network analysis with the areas of pattern recognition and feature selection, as well as on surveying some concepts and measurements from traditional graph theory which are potentially useful for complex network research. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the
Constrained Random Walks on Random Graphs: Routing Algorithms for Large Scale Wireless Sensor Networks
, 2002
"... We consider a routing problem in the context of large scale networks with uncontrolled dynamics. A case of uncontrolled dynamics that has been studied extensively is that of mobile nodes, as this is typically the case in cellular and mobile adhoc networks. In this paper however we study routing in ..."
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Cited by 93 (3 self)
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We consider a routing problem in the context of large scale networks with uncontrolled dynamics. A case of uncontrolled dynamics that has been studied extensively is that of mobile nodes, as this is typically the case in cellular and mobile adhoc networks. In this paper however we study routing in the presence of a different type of dynamics: nodes do not move, but instead switch between active and inactive states at random times. Our interest in this case is motivated by the behavior of sensor nodes powered by renewable sources, such as solar cells or ambient vibrations. In this paper we formalize the corresponding routing problem as a problem of constructing suitably constrained random walks on random dynamic graphs. We argue that these random walks should be designed so that their resulting invariant distribution achieves a certain load balancing property, and we give simple distributed algorithms to compute the local parameters for the random walks that achieve the sought behavior. A truly novel feature of our formulation is that the algorithms we obtain are able to route messages along all possible routes between a source and a destination node, without performing explicit route discovery/repair computations, and without maintaining explicit state information about available routes at the nodes. To the best of our knowledge, these are the first algorithms that achieve true multipath routing (in a statistical sense), at the complexity of simple stateless operations.