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 small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

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.

Betweenness is a measure of the centrality of a node in a network, and is normally calculated as the fraction of shortest paths between node pairs that pass through the node of interest. Betweenness is, in some sense, a measure of the influence a node has over the spread of information through the network. By counting only shortest paths, however, the conventional definition implicitly assumes that information spreads only along those shortest paths. Here we propose a betweenness measure that relaxes this assumption, including contributions from essentially all paths between nodes, not just the shortest, although it still gives more weight to short paths. The measure is based on random walks, counting how often a node is traversed by a random walk between two other nodes. We show how our measure can be calculated using matrix methods, and give some examples of its application to particular networks. 1

Web caches, content distribution networks, peer-to-peer file sharing networks, distributed file systems, and data grids all have in common that they involve a community of users who generate requests for shared data. In each case, overall system performance can be improved significantly if we can first identify and then exploit interesting structure within a community's access patterns. To this end, we propose a novel perspective on file sharing based on the study of the relationships that form among users based on the files in which they are interested. We propose a new structure that captures common user interests in data---the data-sharing graph--- and justify its utility with studies on three data-distribution systems: a high-energy physics collaboration, the Web, and the Kazaa peer-to-peer network. We find small-world patterns in the data-sharing graphs of all three communities. We analyze these graphs and propose some probable causes for these emergent small-world patterns. The significance of smallworld patterns is twofold: it provides a rigorous support to intuition and, perhaps most importantly, it suggests ways to design mechanisms that exploit these naturally emerging patterns.

This article introduces a suite of approaches and measures to study the impact of co-authorship teams based on the number of publications and their citations on a local and global scale. In particular, we present a novel weighted graph representation that encodes coupled author-paper networks as a weighted co-authorship graph. This weighted graph representation is applied to a dataset that captures the emergence of a new field of science and comprises 614 articles published by 1036 unique authors between 1974 and 2004. To characterize the properties and evolution of this field, we first use four different measures of centrality to identify the impact of authors. A global statistical analysis is performed to characterize the distribution of paper production and paper citations and its correlation with the co-authorship team size. The size of co-authorship clusters over time is examined. Finally, a novel local, author-centered measure based on entropy is applied to determine the global evolution of the field and the identification of the contribution of a single author’s impact across all of its co-authorship relations. A visualization of the growth of the weighted co-author network, and the results obtained from the statistical analysis indicate a drift toward a more cooperative, global collaboration process as the main drive in the production of scientific knowledge.

Uncovering the hidden regularities and organizational principles of networks arising in physical systems ranging from the molecular level to the scale of large communication infrastructures is the key issue for the understanding of their fabric and dynamical prop-erties 1,2,3,4,5. The “rich-club ” phenomenon refers to the tendency of nodes with high cen-trality, the dominant elements of the system, to form tightly interconnected communities and it is one of the crucial properties accounting for the formation of dominant communi-ties in both computer and social sciences 4,5,6,7,8. Here we provide the analytical expression and the correct null models which allow for a quantitative discussion of the rich-club phe-nomenon. The presented analysis enables the measurement of the rich-club ordering and its relation with the function and dynamics of networks in examples drawn from the bio-logical, social and technological domains. Recently, the informatics revolution has made possible the analysis of a wide range of large scale, rapidly evolving networks such as transportation, technological, social and biological networks 1,2,3,4,5. While these networks are extremely different from each other in their func-tion and attributes, the analysis of their fabric provided evidence of several shared regularities,

Abstract. We review three studies of information flow in social networks that help reveal their underlying social structure, how information spreads among them and why small world experiments work. 1

It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here the first model which achieves the following challenges: it produces graphs which have the three main wanted properties (clustering, degree distribution, average distance), it is based on some real-world observations, and it is sufficiently simple to make it possible to prove its main properties. This model consists in sampling a random bipartite graph with prescribed degree distribution. Indeed, we show that any complex network can be viewed as a bipartite graph with some specific characteristics, and that its main properties can be viewed as consequences of this underlying structure. We also propose a growing model based on this observation. Introduction.

The genetic programming bibliography aims to be the most complete reference of papers on genetic programming. In addition to locating publications, it contains coauthor and coeditor relationships which have not previously been studied. These reveal some similarities and differences between our field and collaborative social networks in other scientific fields.

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