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A note on jointly modeling edges and node attributes of a network

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  • Cai, Haiyan

Abstract

We are interested in modeling networks in which the connectivity among the nodes and node attributes are random variables and interact with each other. We propose a probabilistic model that allows one to formulate jointly a probability distribution for these variables. This model can be described as a combination of a latent space model and a Gaussian graphical model: given the node variables, the edges will follow independent logistic distributions, with the node variables as covariates; given edges, the node variables will be distributed jointly as multivariate Gaussian, with their conditional covariance matrix depending on the graph induced by the edges. We will present some basic properties of this model, including a connection between this model and a dynamical network process involving both edges and node variables, the marginal distribution of the model for edges as a random graph model, its one-edge conditional distributions, the FKG inequality, and the existence of a limiting distribution for the edges in an infinite graph.

Suggested Citation

  • Cai, Haiyan, 2017. "A note on jointly modeling edges and node attributes of a network," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 54-60.
    • Handle: RePEc:eee:stapro:v:121:y:2017:i:c:p:54-60
    DOI: 10.1016/j.spl.2016.10.014
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    1. Hoff P.D. & Raftery A.E. & Handcock M.S., 2002. "Latent Space Approaches to Social Network Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1090-1098, December.
    2. Mark S. Handcock & Adrian E. Raftery & Jeremy M. Tantrum, 2007. "Model‐based clustering for social networks," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(2), pages 301-354, March.
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    1. Khalilzadeh, Jalayer, 2018. "Demonstration of exponential random graph models in tourism studies: Is tourism a means of global peace or the bottom line?," Annals of Tourism Research, Elsevier, vol. 69(C), pages 31-41.

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