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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 2591 (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.
Structure and evolution of online social networks
 In Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
, 2006
"... In this paper, we consider the evolution of structure within large online social networks. We present a series of measurements of two such networks, together comprising in excess of five million people and ten million friendship links, annotated with metadata capturing the time of every event in the ..."
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Cited by 402 (4 self)
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In this paper, we consider the evolution of structure within large online social networks. We present a series of measurements of two such networks, together comprising in excess of five million people and ten million friendship links, annotated with metadata capturing the time of every event in the life of the network. Our measurements expose a surprising segmentation of these networks into three regions: singletons who do not participate in the network; isolated communities which overwhelmingly display star structure; and a giant component anchored by a wellconnected core region which persists even in the absence of stars. We present a simple model of network growth which captures these aspects of component structure. The model follows our experimental results, characterizing users as either passive members of the network; inviters who encourage offline friends and acquaintances to migrate online; and linkers who fully participate in the social evolution of the network.
Memetracking and the Dynamics of the News Cycle
, 2009
"... Tracking new topics, ideas, and “memes” across the Web has been an issue of considerable interest. Recent work has developed methods for tracking topic shifts over long time scales, as well as abrupt spikes in the appearance of particular named entities. However, these approaches are less well suite ..."
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Cited by 357 (14 self)
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Tracking new topics, ideas, and “memes” across the Web has been an issue of considerable interest. Recent work has developed methods for tracking topic shifts over long time scales, as well as abrupt spikes in the appearance of particular named entities. However, these approaches are less well suited to the identification of content that spreads widely and then fades over time scales on the order of days — the time scale at which we perceive news and events. We develop a framework for tracking short, distinctive phrases that travel relatively intact through online text; developing scalable algorithms for clustering textual variants of such phrases, we identify a broad class of memes that exhibit wide spread and rich variation on a daily basis. As our principal domain of study, we show how such a memetracking approach can provide a coherent representation of the news cycle — the daily rhythms in the news media that have long been the subject of qualitative interpretation but have never been captured accurately enough to permit actual quantitative analysis. We tracked 1.6 million mainstream media sites and blogs over a period of three months with the total of 90 million articles and we find a set of novel and persistent temporal patterns in the news cycle. In particular, we observe a typical lag of 2.5 hours between the peaks of attention to a phrase in the news media and in blogs respectively, with divergent behavior around the overall peak and a “heartbeat”like pattern in the handoff between news and blogs. We also develop and analyze a mathematical model for the kinds of temporal variation that the system exhibits.
Comparing community structure identification
 Journal of Statistical Mechanics: Theory and Experiment
, 2005
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Nunes Amaral. Functional cartography of complex metabolic networks
 Nature
, 2005
"... Highthroughput techniques are leading to an explosive growth in the size of biological databases and creating the opportunity to revolutionize our understanding of life and disease. Interpretation of these data remains, however, a major scientific challenge. Here, we propose a methodology that enab ..."
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Cited by 259 (3 self)
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Highthroughput techniques are leading to an explosive growth in the size of biological databases and creating the opportunity to revolutionize our understanding of life and disease. Interpretation of these data remains, however, a major scientific challenge. Here, we propose a methodology that enables us to extract and display information contained in complex networks 1,2,3. Specifically, we demonstrate that one can (i) find functional modules 4,5 in complex networks, and (ii) classify nodes into universal roles according to their pattern of intra and intermodule connections. The method thus yields a “cartographic representation ” of complex networks. Metabolic networks 6,7,8 are among the most challenging biological networks and, arguably, the ones with more potential for immediate applicability 9. We use our method to analyze the metabolic networks of twelve organisms from three different superkingdoms. We find that, typically, 80 % of the nodes are only connected to other nodes within their respective modules, and that nodes with different roles are affected by different evolutionary constraints and pressures. Remarkably, we
Random graph models of social networks
"... We describe some new exactly solvable models of the structure of social networks, based on random graphs with arbitrary degree distributions. We give models both for simple unipartite networks, such as acquaintance networks, and bipartite networks, such as affiliation networks. We compare the predic ..."
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Cited by 251 (1 self)
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We describe some new exactly solvable models of the structure of social networks, based on random graphs with arbitrary degree distributions. We give models both for simple unipartite networks, such as acquaintance networks, and bipartite networks, such as affiliation networks. We compare the predictions of our models to data for a number of realworld social networks and find that in some cases the models are in remarkable agreement with the data, while in others the agreement is poorer, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.
Statistical properties of community structure in large social and information networks
"... A large body of work has been devoted to identifying community structure in networks. A community is often though of as a set of nodes that has more connections between its members than to the remainder of the network. In this paper, we characterize as a function of size the statistical and structur ..."
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Cited by 243 (14 self)
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A large body of work has been devoted to identifying community structure in networks. A community is often though of as a set of nodes that has more connections between its members than to the remainder of the network. In this paper, we characterize as a function of size the statistical and structural properties of such sets of nodes. We define the network community profile plot, which characterizes the “best ” possible community—according to the conductance measure—over a wide range of size scales, and we study over 70 large sparse realworld networks taken from a wide range of application domains. Our results suggest a significantly more refined picture of community structure in large realworld networks than has been appreciated previously. Our most striking finding is that in nearly every network dataset we examined, we observe tight but almost trivial communities at very small scales, and at larger size scales, the best possible communities gradually “blend in ” with the rest of the network and thus become less “communitylike.” This behavior is not explained, even at a qualitative level, by any of the commonlyused network generation models. Moreover, this behavior is exactly the opposite of what one would expect based on experience with and intuition from expander graphs, from graphs that are wellembeddable in a lowdimensional structure, and from small social networks that have served as testbeds of community detection algorithms. We have found, however, that a generative model, in which new edges are added via an iterative “forest fire” burning process, is able to produce graphs exhibiting a network community structure similar to our observations.
Diffusion kernels on graphs and other discrete input spaces
 in: Proceedings of the 19th International Conference on Machine Learning
, 2002
"... The application of kernelbased learning algorithms has, so far, largely been confined to realvalued data and a few special data types, such as strings. In this paper we propose a general method of constructing natural families of kernels over discrete structures, based on the matrix exponentiation ..."
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Cited by 226 (7 self)
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The application of kernelbased learning algorithms has, so far, largely been confined to realvalued data and a few special data types, such as strings. In this paper we propose a general method of constructing natural families of kernels over discrete structures, based on the matrix exponentiation idea. In particular, we focus on generating kernels on graphs, for which we propose a special class of exponential kernels called diffusion kernels, which are based on the heat equation and can be regarded as the discretization of the familiar Gaussian kernel of Euclidean space.
Computing communities in large networks using random walks
 J. of Graph Alg. and App. bf
, 2004
"... Dense subgraphs of sparse graphs (communities), which appear in most realworld complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advan ..."
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Cited by 225 (2 self)
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Dense subgraphs of sparse graphs (communities), which appear in most realworld complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advantages: it captures well the community structure in a network, it can be computed efficiently, and it can be used in an agglomerative algorithm to compute efficiently the community structure of a network. We propose such an algorithm, called Walktrap, which runs in time O(mn 2) and space O(n 2) in the worst case, and in time O(n 2 log n) and space O(n 2) in most realworld cases (n and m are respectively the number of vertices and edges in the input graph). Extensive comparison tests show that our algorithm surpasses previously proposed ones concerning the quality of the obtained community structures and that it stands among the best ones concerning the running time.