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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 120 (10 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.
Community structure in large networks: Natural cluster sizes and the absence of large welldefined clusters
, 2008
"... A large body of work has been devoted to defining and identifying clusters or communities in social and information networks, i.e., in graphs in which the nodes represent underlying social entities and the edges represent some sort of interaction between pairs of nodes. Most such research begins wit ..."
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Cited by 79 (6 self)
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A large body of work has been devoted to defining and identifying clusters or communities in social and information networks, i.e., in graphs in which the nodes represent underlying social entities and the edges represent some sort of interaction between pairs of nodes. Most such research begins with the premise that a community or a cluster should be thought of as a set of nodes that has more and/or better connections between its members than to the remainder of the network. In this paper, we explore from a novel perspective several questions related to identifying meaningful communities in large social and information networks, and we come to several striking conclusions. Rather than defining a procedure to extract sets of nodes from a graph and then attempt to interpret these sets as a “real ” communities, we employ approximation algorithms for the graph partitioning problem to characterize as a function of size the statistical and structural properties of partitions of graphs that could plausibly be interpreted as communities. In particular, 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. We study over 100 large realworld networks, ranging from traditional and online social networks, to technological and information networks and
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
Report 200813, July 2008ORACLEGUIDED SEARCH IN SORTED MATRICES IMPROVING BALANCED FLOW COMPUTATION
"... Oracleguided search in sorted matrices improving balanced flow compuatation ..."
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Oracleguided search in sorted matrices improving balanced flow compuatation
ORACLEGUIDED SEARCH IN SORTED MATRICES IMPROVING BALANCED FLOW COMPUTATION
"... Abstract. In a successor search we are given a key x and a set A from a totally ordered universe and search for the smallest element of A that is larger than or equal to x. It is well known that the number of comparisons with x needed for this task changes from Θ(A) to Θ(log A) if A is stored in ..."
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Abstract. In a successor search we are given a key x and a set A from a totally ordered universe and search for the smallest element of A that is larger than or equal to x. It is well known that the number of comparisons with x needed for this task changes from Θ(A) to Θ(log A) if A is stored in sorted order. Here, we consider a related situation where the elements of A are organised as a so called sorted matrix. In such a matrix every column and every row is sorted. Further, x is given implicitly by a “monotone oracle”. Given a test value t, the oracle answers the question whether t ≥ x. We give a search algorithm for a sorted n × nmatrix performing O(log n) calls to the oracle and O(n) comparisons between matrix elements which we prove to be optimal. We extend this result to the case of nonsquare matrices and the situation where only columns are sorted. Our search techniques can be applied as the key tool to give an improved algorithm for the uniform balanced network flow problem (ubnfp). The ubnfp consists of finding a feasible stflow of given value F in a graph G = (V, A) which minimizes the difference of the maximum and the minimum flow on an arc. We show that our search techniques can be applied to obtain an O(log 2 m ·T 2 MF(n, m)) time algorithm for solving the ubnfp, where TMF(n, m) is the time required for a maximum flow computation in a network with n vertices and m arcs. This improves upon the previous best time bound of O(n 2 ·T 2 MF(n, m)).
HP Transforms Product Portfolio Management with Operations Research
"... cost analysis; stochastic inventory analysis; flow algorithms; product portfolio management; inventory ..."
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cost analysis; stochastic inventory analysis; flow algorithms; product portfolio management; inventory