Generalizing Egocentric Temporal Neighborhoods to probe for spatial correlations in temporal networks and infer their topology

TL;DR

This paper introduces edge-centered motifs that include triangles and are scalable for analyzing temporal networks, providing new insights into social interaction dynamics and enabling network topology inference.

Contribution

It proposes a new class of scalable, triangle-inclusive motifs called edge-centered motifs, extending previous egocentric motifs and enabling topology inference in temporal networks.

Findings

Edge-centered motifs subsume egocentric motifs analytically.

Empirical data shows edge-centered motifs provide relevant information.

Motifs can be used to infer the underlying network topology.

Abstract

Motifs are thought to be some fundamental components of social face-to-face interaction temporal networks. However, the motifs previously considered are either limited to a handful of nodes and edges, or do not include triangles, which are thought to be of critical relevance to understand the dynamics of social systems. Thus, we introduce a new class of motifs, that include these triangles, are not limited in their number of nodes or edges, and yet can be mined efficiently in any temporal network. Referring to these motifs as the edge-centered motifs, we show analytically how they subsume the Egocentric Temporal Neighborhoods motifs of the literature. We also confirm in empirical data that the edge-centered motifs bring relevant information with respect to the Egocentric motifs by using a principle of maximum entropy. Then, we show how mining for the edge-centered motifs in a network can be used to probe for spatial correlations in the underlying dynamics that have produced that network. We deduce an approximate formula for the distribution of the edge-centered motifs in empirical networks of social face-to-face interactions. In the last section of this paper, we explore how the statistics of the edge-centered motifs can be used to infer the complete topology of the network they were sampled from. This leads to the needs of mathematical development, that we inaugurate here under the name of graph tiling theory.