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Abstract:
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Similarly to motifs (small subgraph patterns) in static networks, temporal motifs are the fundamental building blocks for temporal structures in dynamic networks consisting of a set of vertices and a collection of timestamped interaction events, i.e., temporal edges, between vertices. Temporal motifs are defined as classes of isomorphic induced subgraphs on sequences of temporal edges, considering both edge ordering and duration. Several methods have been designed to count the occurrences of temporal motifs in dynamic networks, with recent work focusing on estimating the count under various sampling schemes along with concentration properties. However, little attention has been given to the statistical inference framework for the count estimators. In this paper, we provide conditions for the consistency and the asymptotic normality of the Horvitz-Thompson type of estimator in an edge sampling framework, which can be used to construct confidence intervals and hypothesis testing for the temporal motif count in the sampling model. We also discuss these conditions under various stochastic models for dynamic networks with temporal edges from the class of multivariate counting processes.
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