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Communities are a common and widely studied structure in networks, typicallyunder the assumption that the network is fully and correctly observed. Inpractice, network data are often collected by querying nodes about theirconnections. In some settings, all edges of a sampled node will be recorded,and in others, a node may be asked to name its connections. These samplingmechanisms introduce noise and bias which can obscure the community structureand invalidate assumptions underlying standard community detection methods. Wepropose a general model for a class of network sampling mechanisms based onrecording edges via querying nodes, designed to improve community detection fornetwork data collected in this fashion. We model edge sampling probabilities asa function of both individual preferences and community parameters, and showcommunity detection can be performed by spectral clustering under this generalclass of models. We also propose, as a special case of the general framework, aparametric model for directed networks we call the nomination stochastic blockmodel, which allows for meaningful parameter interpretations and can be fittedby the method of moments. Both spectral clustering and the method of moments inthis case are computationally efficient and come with theoretical guarantees ofconsistency. We evaluate the proposed model in simulation studies on bothunweighted and weighted networks and apply it to a faculty hiring dataset,discovering a meaningful hierarchy of communities among US business schools.

Community models for networks observed through edge nominations