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In this paper we show how to efficiently produce unbiased estimates ofsubgraph frequencies from a probability sample of egocentric networks (i.e.,focal nodes, their neighbors, and the induced subgraphs of ties among theirneighbors). A key feature of our proposed method that differentiates it fromprior methods is the use of egocentric data. Because of this, our method issuitable for estimation in large unknown graphs, is easily parallelizable,handles privacy sensitive network data (e.g. egonets with no neighbor labels),and supports counting of large subgraphs (e.g. maximal clique of size 205 inSection 6) by building on top of existing exact subgraph counting algorithmsthat may not support sampling. It gracefully handles a variety of samplingdesigns such as uniform or weighted independence or random walk sampling. Ourmethod can be used for subgraphs that are: (i) undirected or directed; (ii)induced or non-induced; (iii) maximal or non-maximal; and (iv) potentiallyannotated with attributes. We compare our estimators on a variety of real-worldgraphs and sampling methods and provide suggestions for their use. Simulationshows that our method outperforms the state-of-the-art approach for relativesubgraph frequencies by up to an order of magnitude for the same sample size.Finally, we apply our methodology to a rare sample of Facebook users across thesocial graph to estimate and interpret the clique size distribution and gendercomposition of cliques.

Estimating Subgraph Frequencies with or without Attributes from Egocentrically Sampled Data