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Abstract:
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Communities are an important type of structure in networks and they have been widely studied. In practice, network data are often collected through sampling mechanisms, such as survey questionnaires, instead of direct observation. The noise and bias introduced by such sampling mechanisms can obscure the community structure and invalidate the assumptions of standard community detection methods. We propose a model to incorporate neighborhood sampling, through a model reflective of survey designs, into community detection for directed networks, since friendship networks obtained from surveys are naturally directed. We model the edge sampling probabilities as a function of both individual preferences and community parameters, and fit the model by a combination of spectral clustering and the method of moments. The algorithm is computationally efficient and comes with a theoretical guarantee of consistency. We evaluate the proposed model in extensive simulation studies and applied it to a faculty hiring dataset, discovering a meaningful hierarchy of communities among US business schools.
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