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18
Birds of a feather, or friend of a friend?: USING EXPONENTIAL RANDOM GRAPH MODELS TO . . .
, 2009
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Peer influence groups: identifying dense clusters in large networks
 SOCIAL NETWORKS
, 2001
"... Sociologists have seen a dramatic increase in the size and availability of social network data. This represents a poverty of riches, however, since many of our analysis techniques cannot handle the resulting large (tens to hundreds of thousands of nodes) networks. In this paper, I provide a method f ..."
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Sociologists have seen a dramatic increase in the size and availability of social network data. This represents a poverty of riches, however, since many of our analysis techniques cannot handle the resulting large (tens to hundreds of thousands of nodes) networks. In this paper, I provide a method for identifying dense regions within large networks based on a peer influence model. Using software familiar to most sociologists, the method reduces the network to a set of m position variables that can then be used in fast cluster analysis programs. The method is tested against simulated networks with a known smallworld structure showing that the underlying clusters can be accurately recovered. I then compare the performance of the procedure with other subgroup detection algorithms on the MacRea and Gagnon prison friendship data and a larger adolescent friendship network, showing that the algorithm replicates other procedures for small networks and outperforms them on the
Comparing Social Networks: Size, Density, and Local Structure
"... This paper demonstrates limitations in usefulness of the triad census for studying similarities among local structural properties of social networks. A triad census succinctly summarizes the local structure of a network using the frequencies of sixteen isomorphism classes of triads (subgraphs of th ..."
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This paper demonstrates limitations in usefulness of the triad census for studying similarities among local structural properties of social networks. A triad census succinctly summarizes the local structure of a network using the frequencies of sixteen isomorphism classes of triads (subgraphs of three nodes). The empirical base for this study is a collection of 51 social networks measuring different relational contents (friendship, advice, agonistic encounters, victories in fights, dominance relations, and so on) among a variety of species (humans, chimpanzees, hyenas, monkeys, ponies, cows, and a number of bird species). Results show that, in aggregate, similarities among triad censuses of these empirical networks are largely explained by nodal and dyadic properties – the density of the network and distributions of mutual, asymmetric, and null dyads. These results remind us that the range of possible networklevel properties is highly constrained by the size and density of the network and caution should be taken in interpreting higher order structural properties when they are largely explained by local network features. 1
Conditional Maximum Likelihood Estimation under Various Specifications of Exponential Random Graph Models
 Frank. University of Stockholm: Department of Statistics
, 2002
"... This paper considers only models with such a conditioning ..."
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Cited by 15 (9 self)
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This paper considers only models with such a conditioning
Accounting for Degree Distributions in Empirical Analysis of Network Dynamics
 Proceedings of the National Academy of Sciences USA
, 2003
"... Degrees (the number of links attached to a given node) play a particular and important role in empirical network analysis because of their obvious importance for expressing the position of nodes. It is argued here that there is no general straightforward relation between the degree distribution on o ..."
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Degrees (the number of links attached to a given node) play a particular and important role in empirical network analysis because of their obvious importance for expressing the position of nodes. It is argued here that there is no general straightforward relation between the degree distribution on one hand and structural aspects on the other hand, as this relation depends on further characteristics of the presumed model for the network. Therefore empirical inference from observed network characteristics to the processes that could be responsible for network genesis and dynamics cannot be based only, or mainly, on the observed degree distribution.
Mining interesting link formation rules in social networks
 In CIKM ’10
, 2010
"... Link structures are important patterns one looks out for when modeling and analyzing social networks. In this paper, we propose the task of mining interesting Link Formation rules (LFrules) containing link structures known as Link Formation patterns (LFpatterns). LFpatterns capture various dya ..."
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Link structures are important patterns one looks out for when modeling and analyzing social networks. In this paper, we propose the task of mining interesting Link Formation rules (LFrules) containing link structures known as Link Formation patterns (LFpatterns). LFpatterns capture various dyadic and/or triadic structures among groups of nodes, while LFrules capture the formation of a new link from a focal node to another node as a postcondition of existing connections between the two nodes. We devise a novel LFrule mining algorithm, known as LFRMiner, based on frequent subgraph mining for our task. In addition to using a supportconfidence framework for measuring the frequency and significance of LFrules, we introduce the notion of expected support to account for the extent to which LFrules exist in a social network by chance. Specifically, only LFrules with higherthanexpected support are considered interesting. We conduct empirical studies on two realworld social networks, namely Epinions and myGamma. We report interesting LFrules mined from the two networks, and compare our findings with earlier findings in social network analysis.
Markov chain Monte Carlo exact inference for social networks
 Social Networks
, 2007
"... We propose modifications to existing Markov chain Monte Carlo algorithms to generate from the conditional distribution of an adjacency matrix, given the indegrees, the outdegrees and the number of mutual dyads. We compare our results with those obtained by using various approximations. ..."
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We propose modifications to existing Markov chain Monte Carlo algorithms to generate from the conditional distribution of an adjacency matrix, given the indegrees, the outdegrees and the number of mutual dyads. We compare our results with those obtained by using various approximations.