Generalized blockmodeling of valued networks

Žiberna, Aleš

doi:10.1016/j.socnet.2006.04.002

Cited by 69 publications

(39 citation statements)

References 18 publications

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“…It is freely available, for non-commercial use, at: http://pajek.imfm.si. All calculations besides clustering were made with using R and some visualizations were made with an R package for Generalized and classical blockmodeling of valued networks (Ziberna 2007).…”

Section: Softwarementioning

confidence: 99%

On the dynamics of national scientific systems

2011

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Section: Softwarementioning

confidence: 99%

On the dynamics of national scientific systems

2011

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“…Our approach builds on these latter references. We also point out the existence of generalized block models for valued networks (Ziberna, 2007; Doreian et al. , 2005) which, however, do not rely on a probabilistic model as we shall do here.…”

Section: Introductionmentioning

confidence: 97%

New Consistent and Asymptotically Normal Parameter Estimates for Random-Graph Mixture Models

Ambroise

Matias

2011

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Random-graph mixture models are very popular for modelling real data networks. Parameter estimation procedures usually rely on variational approximations, either combined with the expectation-maximization (EM) algorithm or with Bayesian approaches. Despite good results on synthetic data, the validity of the variational approximation is, however, not established. Moreover, these variational approaches aim at approximating the maximum likelihood or the maximum a posteriori estimators, whose behaviour in an asymptotic framework (as the sample size increases to ∞) remains unknown for these models. In this work, we show that, in many different affiliation contexts (for binary or weighted graphs), parameter estimators based either on moment equations or on the maximization of some composite likelihood are strongly consistent and p n convergent, when the number n of nodes increases to ∞. As a consequence, our result establishes that the overall structure of an affiliation model can be (asymptotically) caught by the description of the network in terms of its number of triads (order 3 structures) and edges (order 2 structures). Moreover, these parameter estimates are either explicit (as for the moment estimators) or may be approximated by using a simple EM algorithm, whose convergence properties are known. We illustrate the efficiency of our method on simulated data and compare its performances with other existing procedures. A data set of cross-citations among economics journals is also analysed.

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“…Instead of allowing only oneblocks and zeroblocks, they also considered modeling networks by other types of role blocks, e.g., dominant blocks where at least one individual from one position is connected to everyone in the other position, and regular blocks where everyone in one position is connected to at least one individual from the other position. Ziberna [19] further generalized this idea to valued networks, which aims to minimize the inconsistency among edges grouped into each role block.…”

Section: Related Workmentioning

confidence: 99%

Structural Analysis in Multi-Relational Social Networks

Dai

Chua

Lim

2012

Proceedings of the 2012 SIAM International Conference on Data Mining

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Modern social networks often consist of multiple relations among individuals. Understanding the structure of such multi-relational network is essential. In sociology, one way of structural analysis is to identify different positions and roles using blockmodels. In this paper, we generalize stochastic blockmodels to Generalized Stochastic Blockmodels (GSBM) for performing positional and role analysis on multi-relational networks. Our GSBM generalizes many different kinds of Multivariate Probability Distribution Function (MVPDF) to model different kinds of multi-relational networks. In particular, we propose to use multivariate Poisson distribution for multi-relational social networks. Our experiments show that GSBM is able to identify the structures for both synthetic and real world network data. These structures can further be used for predicting relationships between individuals.

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Generalized blockmodeling of valued networks

Cited by 69 publications

References 18 publications

On the dynamics of national scientific systems

On the dynamics of national scientific systems

New Consistent and Asymptotically Normal Parameter Estimates for Random-Graph Mixture Models

Structural Analysis in Multi-Relational Social Networks

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