Estimation and Prediction for Stochastic Blockmodels for Graphs with Latent Block Structure

Snijders, Tom A. B.; Nowicki, Krzysztof

doi:10.1007/s003579900004

Cited by 517 publications

(441 citation statements)

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“…As mentioned above this fits into a rich literature on estimating community structures from network data (again, for overviews see Wasserman and Faust (1994), Snijders and Nowicki (1997), Newman (2003), and Jackson (2008)). The contribution here is to begin a program of characterizing different techniques based on their properties, and also to base a technique on an underlying model of what community structures are and how they lead to network formation.…”

Section: Relation To the Literaturesupporting

confidence: 63%

Identifying Community Structures from Network Data via Maximum Likelihood Methods

Čopič

Jackson

Kirman

2009

The B.E. Journal of Theoretical Economics

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Networks of social and economic interactions are often influenced by unobserved structures among the nodes. Based on a simple model of how an unobserved community structure generates networks of interactions, we axiomatize a method of detecting the latent community structures from network data. The method is based on maximum likelihood estimation. * Č opič is the department of economics at UCLA,

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Section: Relation To the Literaturesupporting

confidence: 63%

Identifying Community Structures from Network Data via Maximum Likelihood Methods

Čopič

Jackson

Kirman

2009

The B.E. Journal of Theoretical Economics

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“…Early approaches such as QAP regression may work as a first approximation, but they rest on the somewhat dubious assumption of dyadic independence (see Alderson and Beckfield 2004 for a recent application). Recent advances in statistical network models including the exponential random graph (ERG) model (Anderson, Wasserman and Crouch 1999;Contractor, Wasserman and Faust 2006;Holland and Leinhardt 1975;1981, Robins andMorris 2007) or the stochastic block model (see Wasserman and Faust 1994: 675-723 for a general introduction; Nowicki and Snijders 2001;Snijders and Nowicki 1997;Wang and Wong 1987) may take us in the right direction.…”

Section: Resultsmentioning

confidence: 99%

Looking Back and Forging Ahead: Thirty Years of Social Network Research on the World-System

Lloyd

Mahutga

Leeuw

2009

JWSR

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“…Block modelling [63][64][65][66][67] is in effect a form of statistical inference for networks. In the same way that we can gain some understanding from conventional numerical data by fitting, say, a straight line through data points, so we can gain understanding of the structure of networks by fitting them to a statistical network model.…”

Section: Block Modelsmentioning

confidence: 99%

Communities, modules and large-scale structure in networks

2011

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Networks, also called graphs by mathematicians, provide a useful abstraction of the structure of many complex systems, ranging from social systems and computer networks to biological networks and the state spaces of physical systems. In the past decade there have been significant advances in experiments to determine the topological structure of networked systems, but there remain substantial challenges in extracting scientific understanding from the large quantities of data produced by the experiments. A variety of basic measures and metrics are available that can tell us about small-scale structure in networks, such as correlations, connections and recurrent patterns, but it is considerably more difficult to quantify structure on medium and large scales, to understand the 'big picture'. Important progress has been made, however, within the past few years, a selection of which is reviewed here.A network is, in its simplest form, a collection of dots joined together in pairs by lines (Fig. 1). In the jargon of the field, a dot is called a 'node' or 'vertex' (plural 'vertices') and a line is called an 'edge'. Networks are used in many branches of science as a way to represent the patterns of connections between the components of complex systems [1][2][3][4][5][6] . Examples include the Internet 7,8 , in which the nodes are computers and the edges are data connections such as optical-fibre cables, food webs in biology 9,10 , in which the nodes are species in an ecosystem and the edges represent predator-prey interactions, and social networks 11,12 , in which the nodes are people and the edges represent any of a variety of different types of social interaction including friendship, collaboration, business relationships or others.In the past decade there has been a surge of interest in both empirical studies of networks 13 and development of mathematical and computational tools for extracting insight from network data 1-6 . One common approach to the study of networks is to focus on the properties of individual nodes or small groups of nodes, asking questions such as, 'Which is the most important node in this network?' or 'Which are the strongest connections?' Such approaches, however, tell us little about large-scale network structure. It is this large-scale structure that is the topic of this paper.The best-studied form of large-scale structure in networks is modular or community structure 14,15 . A community, in this context, is a dense subnetwork within a larger network, such as a close-knit group of friends in a social network or a group of interlinked web pages on the World Wide Web (Fig. 1). Although communities are not the only interesting form of large-scale structure-there are others that we will come to-they serve as a good illustration of the nature and scope of present research in this area and will be our primary focus.Communities are of interest for a number of reasons. They have intrinsic interest because they may correspond to functional units within a networked system, an example of the kind of link...

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Estimation and Prediction for Stochastic Blockmodels for Graphs with Latent Block Structure

Cited by 517 publications

References 0 publications

Identifying Community Structures from Network Data via Maximum Likelihood Methods

Identifying Community Structures from Network Data via Maximum Likelihood Methods

Looking Back and Forging Ahead: Thirty Years of Social Network Research on the World-System

Communities, modules and large-scale structure in networks

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