Results 11  20
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90
Analyzing Kleinberg’s (and other) smallworld models
 in Proc. of ACM Symp. on Princ. of Dist. Comp. (PODC
, 2004
"... We analyze the properties of SmallWorld networks, where links are much more likely to connect “neighbor nodes ” than distant nodes. In particular, our analysis provides new results for Kleinberg’s SmallWorld model and its extensions. Kleinberg adds a number of directed longrange random links to a ..."
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Cited by 57 (6 self)
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We analyze the properties of SmallWorld networks, where links are much more likely to connect “neighbor nodes ” than distant nodes. In particular, our analysis provides new results for Kleinberg’s SmallWorld model and its extensions. Kleinberg adds a number of directed longrange random links to an n × n lattice network (vertices as nodes of a grid, undirected edges between any two adjacent nodes). Links have a nonuniform distribution that favors arcs to close nodes over more distant ones. He shows that the following phenomenon occurs: between any two nodes a path with expected length O(log 2 n) can be found using a simple greedy algorithm which has no global knowledge of longrange links. We show that Kleinberg’s analysis is tight: his algorithm achieves θ(log 2 n) delivery time. Moreover, we show that the expected diameter of the graph is θ(log n), a log n factor
A framework for analysis of dynamic social networks
 DIMACS Technical Report
, 2006
"... Finding patterns of social interaction within a population has wideranging applications including: disease modeling, cultural and information transmission, and behavioral ecology. Social interactions are often modeled with networks. A key characteristic of social interactions is their continual cha ..."
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Cited by 53 (10 self)
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Finding patterns of social interaction within a population has wideranging applications including: disease modeling, cultural and information transmission, and behavioral ecology. Social interactions are often modeled with networks. A key characteristic of social interactions is their continual change. However, most past analyses of social networks are essentially static in that all information about the time that social interactions take place is discarded. In this paper, we propose a new mathematical and computational framework that enables analysis of dynamic social networks and that explicitly makes use of information about when social interactions occur.
The darknet and the future of content distribution
 In Proceedings of the 2002 ACM Workshop on Digital Rights Management
, 2002
"... ..."
Local search in unstructured networks
 Handbook of Graphs and Networks
, 2003
"... Recently, studies of networks in a wide variety of fields, from biology to social science to computer science, have revealed some commonalities [4]. It has become clear that the simplest classical model of random networks, the ErdosRenyi model [8], is inadequate for describing the topology of many ..."
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Cited by 24 (0 self)
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Recently, studies of networks in a wide variety of fields, from biology to social science to computer science, have revealed some commonalities [4]. It has become clear that the simplest classical model of random networks, the ErdosRenyi model [8], is inadequate for describing the topology of many naturally occurring networks. These diverse networks are more
Information Dynamics in the Networked World
 In Lecture Notes in Physics
, 2004
"... Summary. We review three studies of information flow in social networks that help reveal their underlying social structure, how information spreads through them and why small world experiments work. 1 ..."
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Cited by 24 (3 self)
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Summary. We review three studies of information flow in social networks that help reveal their underlying social structure, how information spreads through them and why small world experiments work. 1
Mixing patterns and community structure in networks
 in Statistical Mechanics of Complex Networks
"... Common experience suggests that many networks might possess community structure—division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects structure of this kind. We apply the algorithm to a number of realw ..."
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Cited by 21 (1 self)
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Common experience suggests that many networks might possess community structure—division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects structure of this kind. We apply the algorithm to a number of realworld networks and show that they do indeed possess nontrivial community structure. We suggest a possible explanation for this structure in the mechanism of assortative mixing, which is the preferential association of network vertices with others that are like them in some way. We show by simulation that this mechanism can indeed account for community structure. We also look in detail at one particular example of assortative mixing, namely mixing by vertex degree, in which vertices with similar degree prefer to be connected to one another. We propose a measure for mixing of this type which we apply to a variety of networks, and also discuss the implications for network structure and the formation of a giant component in assortatively mixed networks. 1
Stochastic kronecker graphs
 Proceedings of the 5th Workshop on Algorithms and Models for the WebGraph
, 2007
"... A random graph model based on Kronecker products of probability matrices has been recently proposed as a generative model for largescale realworld networks such as the web. This model simultaneously captures several wellknown properties of realworld networks; in particular, it gives rise to a he ..."
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Cited by 19 (2 self)
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A random graph model based on Kronecker products of probability matrices has been recently proposed as a generative model for largescale realworld networks such as the web. This model simultaneously captures several wellknown properties of realworld networks; in particular, it gives rise to a heavytailed degree distribution, has a low diameter, and obeys the densification power law. Most properties of Kronecker products of graphs (such as connectivity and diameter) are only rigorously analyzed in the deterministic case. In this paper, we study the basic properties of stochastic Kronecker products based on an initiator matrix of size two (which is the case that is shown to provide the best fit to many realworld networks). We will show a phase transition for the emergence of the giant component and another phase transition for connectivity, and prove that such graphs have constant diameters beyond the connectivity threshold, but are not searchable using a decentralized algorithm. 1
Distributed Routing in SmallWorld Networks
, 2007
"... So called smallworld networks – clustered networks with small diameters – are thought to be prevalent in nature, especially appearing in people’s social interactions. Many models exist for this phenomenon, with some of the most recent explaining how it is possible to find short routes between nodes ..."
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Cited by 18 (3 self)
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So called smallworld networks – clustered networks with small diameters – are thought to be prevalent in nature, especially appearing in people’s social interactions. Many models exist for this phenomenon, with some of the most recent explaining how it is possible to find short routes between nodes in such networks. Searching for such routes, however, always depends on nodes knowing what their and their neighbors positions are relative to the destination. In real applications where one may wish to search a smallworld network, such as peertopeer computer networks, this cannot always be assumed to be true. We propose and explore a method of routing that does not depend on such knowledge, and which can be implemented in a completely distributed way without any global elements. The Markov Chain MonteCarlo based algorithm takes only a graph as input, and requires no further information about the nodes themselves. The proposed method is tested against simulated and real world data.
Towards small world emergence
 In Proceedings of 18th ACM Symposium on Parallelism in Algorithms and Architectures
, 2006
"... We investigate the problem of optimizing the routing performances of a virtual network by adding extra random links. Our asynchronous and distributed algorithm ensures, by adding a single extra link per node, that the resulting network is a navigable small world, i.e., in which greedy routing, using ..."
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Cited by 18 (3 self)
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We investigate the problem of optimizing the routing performances of a virtual network by adding extra random links. Our asynchronous and distributed algorithm ensures, by adding a single extra link per node, that the resulting network is a navigable small world, i.e., in which greedy routing, using the distance in the original network, computes paths of polylogarithmic length between any pair of nodes with probability 1 − O(1/n). Previously known small world augmentation processes require the global knowledge of the network and centralized computations, which is unrealistic for large decentralized networks. Our algorithm, based on a careful multilayer sampling of the nodes and the construction of a light overlay network, bypasses these limitations. For bounded growth graphs, i.e., graphs where, for any node u and any radius r the number of nodes within distance 2r from u is at most a constant times the number of nodes within distance r, our augmentation process proceeds with high probability in O(log n log D) communication rounds, with O(log n log D) messages of size O(log n) bits sent per node and requiring only O(log n log D) bit space in each node, where n is the number of nodes, and D the diameter. In particular, with the only knowledge of original distances, greedy routing computes,
Dynamics of Large Networks
, 2008
"... A basic premise behind the study of large networks is that interaction leads to complex collective behavior. In our work we found very interesting and counterintuitive patterns for time evolving networks, which change some of the basic assumptions that were made in the past. We then develop models ..."
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Cited by 18 (0 self)
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A basic premise behind the study of large networks is that interaction leads to complex collective behavior. In our work we found very interesting and counterintuitive patterns for time evolving networks, which change some of the basic assumptions that were made in the past. We then develop models that explain processes which govern the network evolution, fit such models to real networks, and use them to generate realistic graphs or give formal explanations about their properties. In addition, our work has a wide range of applications: it can help us spot anomalous graphs and outliers, forecast future graph structure and run simulations of network evolution. Another important aspect of our research is the study of “local ” patterns and structures of propagation in networks. We aim to identify building blocks of the networks and find the patterns of influence that these blocks have on information or virus propagation over the network. Our recent work included the study of the spread of influence in a large persontoperson