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1,036
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 252 (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 real-world 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 246 (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 real-world networks taken from a wide range of application domains. Our results suggest a significantly more refined picture of community structure in large real-world 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 “community-like.” This behavior is not explained, even at a qualitative level, by any of the commonly-used 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 well-embeddable in a low-dimensional 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.
Geographic routing in social networks
, 2005
"... We live in a “small world,” where two arbitrary people are likely connected by a short chain of intermediate friends. With scant information about a target individual, people can successively forward a message along such a chain. Experimental studies have verified this property in real social networ ..."
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Cited by 232 (10 self)
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We live in a “small world,” where two arbitrary people are likely connected by a short chain of intermediate friends. With scant information about a target individual, people can successively forward a message along such a chain. Experimental studies have verified this property in real social networks, and theoretical models have been advanced to explain it. However, existing theoretical models have not been shown to capture behavior in real-world social networks. Here we introduce a richer model relating geography and social-network friendship, in which the probability of befriending a particular person is inversely proportional to the number of closer people. In a large social network, we show that one third of the friendships are independent of geography, and the remainder exhibit the proposed relationship. Further, we prove analytically that short chains can be discovered in every network exhibiting the relationship.
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 real-world 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 226 (3 self)
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Dense subgraphs of sparse graphs (communities), which appear in most real-world 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 real-world 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.
SybilLimit: A nearoptimal social network defense against sybil attacks
- 2008 [Online]. Available: http://www.comp.nus.edu.sg/~yuhf/sybillimit-tr.pdf
"... Abstract—Open-access distributed systems such as peer-to-peer systems are particularly vulnerable to sybil attacks, where a malicious user creates multiple fake identities (called sybil nodes). Without a trusted central authority that can tie identities to real human beings, defending against sybil ..."
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Cited by 216 (7 self)
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Abstract—Open-access distributed systems such as peer-to-peer systems are particularly vulnerable to sybil attacks, where a malicious user creates multiple fake identities (called sybil nodes). Without a trusted central authority that can tie identities to real human beings, defending against sybil attacks is quite challenging. Among the small number of decentralized approaches, our recent SybilGuard protocol leverages a key insight on social networks to bound the number of sybil nodes accepted. Despite its promising direction, SybilGuard can allow a large number of sybil nodes to be accepted. Furthermore, SybilGuard assumes that social networks are fast-mixing, which has never been confirmed in the real world. This paper presents the novel SybilLimit protocol that leverages the same insight as SybilGuard, but offers dramatically improved and near-optimal guarantees. The number of sybil nodes accepted is reduced by a factor of 2 ( p n), or around 200 times in our experiments for a million-node system. We further prove that SybilLimit’s guarantee is at most a log n factor away from optimal when considering approaches based on fast-mixing social networks. Finally, based on three large-scale real-world social networks, we provide the first evidence that real-world social networks are indeed fast-mixing. This validates the fundamental assumption behind SybilLimit’s and SybilGuard’s approach. Index Terms—Social networks, sybil attack, sybil identities, SybilGuard, SybilLimit. I.
Community structure in large networks: Natural cluster sizes and the absence of large well-defined 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 208 (17 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 real-world networks, ranging from traditional and on-line social networks, to technological and information networks and
Collaboration and creativity: The small world problem
, 2005
"... Small world networks have received disproportionate notice in diverse fields because of their suspected effect on system dynamics. The authors analyzed the small world network of the creative artists who made Broadway musicals from 1945 to 1989. Using original arguments, new statistical methods, and ..."
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Cited by 207 (10 self)
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Small world networks have received disproportionate notice in diverse fields because of their suspected effect on system dynamics. The authors analyzed the small world network of the creative artists who made Broadway musicals from 1945 to 1989. Using original arguments, new statistical methods, and tests of construct validity, they found that the varying “small world ” properties of the systemic-level network of these artists affected their creativity in terms of the financial and artistic performance of the musicals they produced. The small world network effect was parabolic; performance increased up to a threshold, after which point the positive effects reversed.
Feedback Effects between Similarity and Social Influence in Online Communities
"... A fundamental open question in the analysis of social networks is to understand the interplay between similarity and social ties. People are similar to their neighbors in a social network for two distinct reasons: first, they grow to resemble their current friends due to social influence; and second ..."
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Cited by 164 (8 self)
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A fundamental open question in the analysis of social networks is to understand the interplay between similarity and social ties. People are similar to their neighbors in a social network for two distinct reasons: first, they grow to resemble their current friends due to social influence; and second, they tend to form new links to others who are already like them, a process often termed selection by sociologists. While both factors are present in everyday social processes, they are in tension: social influence can push systems toward uniformity of behavior, while selection can lead to fragmentation. As such, it is important to understand the relative effects of these forces, and this has been a challenge due to the difficulty of isolating and quantifying them in real settings. We develop techniques for identifying and modeling the interactions between social influence and selection, using data from online communities where both social interaction and changes in behavior over time can be measured. We find clear feedback effects between the two factors, with rising similarity between two individuals serving, in aggregate, as an indicator of future interaction — but with similarity then continuing to increase steadily, although at a slower rate, for long periods after initial interactions. We also consider the relative value of similarity and social influence in modeling future behavior. For instance, to predict the activities that an individual is likely to do next, is it more useful to know
Influential Nodes in a Diffusion Model for Social Networks
- IN ICALP
, 2005
"... We study the problem of maximizing the expected spread of an innovation or behavior within a social network, in the presence of "word-of-mouth" referral. Our work builds on the observation that individuals' decisions to purchase a product or adopt an innovation are strongly influe ..."
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Cited by 152 (3 self)
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We study the problem of maximizing the expected spread of an innovation or behavior within a social network, in the presence of "word-of-mouth" referral. Our work builds on the observation that individuals' decisions to purchase a product or adopt an innovation are strongly influenced by recommendations from their friends and acquaintances. Understanding
Preserving privacy in social networks against neighborhood attacks
- In Data Engineering, 2008. ICDE 2008. IEEE 24th International Conference on
, 2008
"... Abstract — Recently, as more and more social network data has been published in one way or another, preserving privacy in publishing social network data becomes an important con-cern. With some local knowledge about individuals in a social network, an adversary may attack the privacy of some victims ..."
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Cited by 134 (4 self)
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Abstract — Recently, as more and more social network data has been published in one way or another, preserving privacy in publishing social network data becomes an important con-cern. With some local knowledge about individuals in a social network, an adversary may attack the privacy of some victims easily. Unfortunately, most of the previous studies on privacy preservation can deal with relational data only, and cannot be applied to social network data. In this paper, we take an initiative towards preserving privacy in social network data. We identify an essential type of privacy attacks: neighborhood attacks. If an adversary has some knowledge about the neighbors of a target victim and the relationship among the neighbors, the victim may be re-identified from a social network even if the victim’s identity is preserved using the conventional anonymization techniques. We show that the problem is challenging, and present a practical solution to battle neighborhood attacks. The empirical study indicates that anonymized social networks generated by our method can still be used to answer aggregate network queries with high accuracy. I.
