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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 2148 (11 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 821 (1 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
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 t ..."
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Cited by 435 (12 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,
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 319 (17 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.
Gossip-based 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 271 (43 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; load-balancing protocols may benefit from knowing the target average load so as to minimize the load they transfer. We propose a gossip-based 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
Networks, Dynamics, and the Small-World Phenomenon
- American Journal of Sociology
, 1999
"... The small-world 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 220 (1 self)
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The small-world 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.
The spread of behavior in an online social network experiment,”
- Science
, 2010
"... How do social networks affect the spread of behavior? A popular hypothesis states that networks with many clustered ties and a high degree of separation will be less effective for behavioral diffusion than networks in which locally redundant ties are rewired to provide shortcuts across the social s ..."
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Cited by 213 (4 self)
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How do social networks affect the spread of behavior? A popular hypothesis states that networks with many clustered ties and a high degree of separation will be less effective for behavioral diffusion than networks in which locally redundant ties are rewired to provide shortcuts across the social space. A competing hypothesis argues that when behaviors require social reinforcement, a network with more clustering may be more advantageous, even if the network as a whole has a larger diameter. I investigated the effects of network structure on diffusion by studying the spread of health behavior through artificially structured online communities. Individual adoption was much more likely when participants received social reinforcement from multiple neighbors in the social network. The behavior spread farther and faster across clustered-lattice networks than across corresponding random networks.
The Large-Scale Structure of Semantic Networks: Statistical Analyses and a Model of Semantic Growth
- Cognitive Science
"... We present statistical analyses of the large-scale structure of three types of semantic networks: word associations, WordNet, and Roget's thesaurus. We show that they have a small-world structure, characterized by sparse connectivity, short average path-lengths between words, and strong local ..."
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Cited by 209 (2 self)
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We present statistical analyses of the large-scale structure of three types of semantic networks: word associations, WordNet, and Roget's thesaurus. We show that they have a small-world structure, characterized by sparse connectivity, short average path-lengths between words, and strong local clustering. In addition, the distributions of the number of connections follow power laws that indicate a scale-free 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 high-dimensional 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 small-world statistics and power-law connectivity distributions, and also suggests one possible mechanistic basis for the effects of learning history variables (age-ofacquisition, usage frequency) on behavioral performance in semantic processing tasks.
Collaboration and creativity: The small world problem
, 2005
"... Small world networks have received disproportionate notice in diverse fields because of their suspected effect on system dynamics. The authors analyzed the small world network of the creative artists who made Broadway musicals from 1945 to 1989. Using original arguments, new statistical methods, and ..."
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Cited by 207 (10 self)
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Small world networks have received disproportionate notice in diverse fields because of their suspected effect on system dynamics. The authors analyzed the small world network of the creative artists who made Broadway musicals from 1945 to 1989. Using original arguments, new statistical methods, and tests of construct validity, they found that the varying “small world ” properties of the systemic-level network of these artists affected their creativity in terms of the financial and artistic performance of the musicals they produced. The small world network effect was parabolic; performance increased up to a threshold, after which point the positive effects reversed.
Computing and Applying Trust in Web-based Social Networks
, 2005
"... The proliferation of web-based 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 web-based social networks, how it can be computed, and how ..."
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Cited by 205 (16 self)
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The proliferation of web-based 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 web-based 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 web-based 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
