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216
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 2600 (7 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.
Power laws, Pareto distributions and Zipf’s law
"... Many of the things that scientists measure have a typical size or “scale”—a typical value around which individual measurements are centred. A simple example would be the heights of human beings. Most adult human beings are about 180cm tall. There is some variation around this figure, notably dependi ..."
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Cited by 413 (0 self)
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Many of the things that scientists measure have a typical size or “scale”—a typical value around which individual measurements are centred. A simple example would be the heights of human beings. Most adult human beings are about 180cm tall. There is some variation around this figure, notably depending on sex, but we never see people who are 10cm tall, or 500cm. To make this observation more quantitative, one can plot a histogram of people’s heights, as I have done in Fig. 1a. The figure shows the heights in centimetres of adult men in the United States measured between 1959 and 1962, and indeed the distribution is relatively narrow and peaked around 180cm. Another telling observation is the ratio of the heights of the tallest and shortest people.
Coauthorship networks and patterns of scientific collaboration
 In Proceedings of the National Academy of Sciences
, 2004
"... Using data from three bibliographic databases in biology, physics, and mathematics respectively, networks are constructed in which the nodes are scientists and two scientists are connected if they have coauthored a paper together. We use these networks to answer a broad variety of questions about co ..."
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Cited by 224 (0 self)
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Using data from three bibliographic databases in biology, physics, and mathematics respectively, networks are constructed in which the nodes are scientists and two scientists are connected if they have coauthored a paper together. We use these networks to answer a broad variety of questions about collaboration patterns, such as the numbers of papers authors write, how many people they write them with, what the typical distance between scientists is through the network, and how patterns of collaboration vary between subjects and over time. We also summarize a number of recent results by other authors on coauthorship patterns. 1
Graph mining: laws, generators, and algorithms
 ACM COMPUT SURV (CSUR
, 2006
"... How does the Web look? How could we tell an abnormal social network from a normal one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks to sociology to biology and many more. Indeed, any M: N relation in ..."
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Cited by 132 (7 self)
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How does the Web look? How could we tell an abnormal social network from a normal one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks to sociology to biology and many more. Indeed, any M: N relation in database terminology can be represented as a graph. A lot of these questions boil down to the following: “How can we generate synthetic but realistic graphs? ” To answer this, we must first understand what patterns are common in realworld graphs and can thus be considered a mark of normality/realism. This survey give an overview of the incredible variety of work that has been done on these problems. One of our main contributions is the integration of points of view from physics, mathematics, sociology, and computer science. Further, we briefly describe recent advances on some related and interesting graph problems.
The Economics of Social Networks.
 In Advances in Economics and Econometrics, Theory and Applications: Ninth World Congress of the Econometric Society.
, 2006
"... Abstract We analyze the problem of optimal monopoly pricing in social networks in order to characterize the influence of the network topology on the pricing rule. It is shown that this influence depends on the type of providers (local versus global monopoly) and of externalities (consumption versus ..."
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Cited by 118 (2 self)
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Abstract We analyze the problem of optimal monopoly pricing in social networks in order to characterize the influence of the network topology on the pricing rule. It is shown that this influence depends on the type of providers (local versus global monopoly) and of externalities (consumption versus price). We identify two situations where the monopolist does not discriminate across nodes in the network (global monopoly with consumption externalities and local monopoly with price externalities) and characterize the relevant centrality index used to discriminate among nodes in the other situations. We also analyze the robustness of the analysis with respect to changes in demand, and the introduction of bargaining between the monopolist and the consumer. JEL Classification Numbers: D85, D43, C69 Keywords: Social Networks, Monopoly Pricing, Network Externalities, Reference Price, Centrality Measures * We dedicate this paper to the memory of Toni CalvóArmengol, a gifted network theorist and a wonderful friend. We thank Coralio Ballester,
Cumulative advantage as a mechanism for inequality: A review of theoretical and empirical development
 Annual Review of Sociology
, 2006
"... While originally developed by Merton to explain advancement in scienti c careers, cumulative advantage is a general mechanism for inequality across any temporal process (e.g., life course, family generations) in which a favorable relative position becomes a resource that produces further relative ..."
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Cited by 86 (3 self)
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While originally developed by Merton to explain advancement in scienti c careers, cumulative advantage is a general mechanism for inequality across any temporal process (e.g., life course, family generations) in which a favorable relative position becomes a resource that produces further relative gains. We show that the term "cumulative advantage " has come to have multiple meanings in the sociological literature. We distinguish between these alternative forms, discuss mechanisms that have been proposed in the literature that might produce cumulative advantage, and review the empirical literature in the areas of education, work careers, and related life course processes.
Creative productivity: A predictive and explanatory model of career trajectories and landmarks
 Psych. Rev
, 1997
"... The author developed a model that explains and predicts both longitudinal and crosssectional variation in the output of major and minor creative products. The model first yields a mathematical equation that accounts for the empirical age curves, including contrasts across creative domains in the ex ..."
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Cited by 65 (5 self)
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The author developed a model that explains and predicts both longitudinal and crosssectional variation in the output of major and minor creative products. The model first yields a mathematical equation that accounts for the empirical age curves, including contrasts across creative domains in the expected career trajectories. The model is then extended to account for individual differences in career trajectories, such as the longitudinal stability of crosssectional variation and the differential placement of career landmarks (the ages at first, best, and last contribution). The theory is parsimonious in that it requires only two individualdifference parameters (initial creative potential and age at career onset) and two informationprocessing parameters (ideation and elaboration rates), plus a single principle (the equalodds rule), to derive several precise predictions that cannot be generated by any alternative theory. Albert Einstein had around 248 publications to his credit, Charles Darwin had 119, and Sigmund Freud had 330, while Thomas Edison held 1,093 patents—still the record granted to any one person by the U.S. Patent Office. Similarly, Pablo Picasso executed more than 20,000 paintings, drawings, and
Counting graph homomorphisms
 IN:TOPICS IN DISCRETE MATH
, 2006
"... Counting homomorphisms between graphs (often with weights) comes up in a wide variety of areas, including extremal graph theory, properties of graph products, partition functions in statistical physics and property testing of large graphs. In this paper we survey recent developments in the study of ..."
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Cited by 58 (16 self)
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Counting homomorphisms between graphs (often with weights) comes up in a wide variety of areas, including extremal graph theory, properties of graph products, partition functions in statistical physics and property testing of large graphs. In this paper we survey recent developments in the study of homomorphism numbers, including the characterization of the homomorphism numbers in terms of the semidefiniteness of “connection matrices”, and some applications of this fact in extremal graph theory. We define a distance of two graphs in terms of similarity of their global structure, which also reflects the closeness of (appropriately scaled) homomorphism numbers into the two graphs. We use homomorphism numbers to define convergence of a sequence of graphs, and show that a graph sequence is convergent if and only if it is Cauchy in this distance. Every convergent graph sequence has a limit in the form of a symmetric measurable function in two variables. We use these notions of distance and graph limits to give a general theory for parameter testing. The convergence can also be characterized in terms of mappings of the graphs into fixed small graphs, which is strongly connected to important parameters like ground state energy in statistical physics, and to weighted maximum cut problems in computer science.
Multilayer networks
 TOOL FOR MULTILAYER ANALYSIS AND VISUALIZATION OF NETWORKS 17 OF 18
, 2014
"... In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is impo ..."
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Cited by 34 (7 self)
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In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such “multilayer” features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize “traditional ” network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary