Node-Specific Triad Pattern Mining for Complex-Network Analysis

The mining of graphs in terms of their local substructure is a well-established methodology to analyze networks. It was hypothesized that motifs - subgraph patterns which appear significantly more often than expected at random - play a key role for the ability of a system to perform its task. Yet the framework commonly used for motif-detection averages over the local environments of all nodes. Therefore, it remains unclear whether motifs are overrepresented in the whole system or only in certain regions. In this contribution, we overcome this limitation by mining node-specific triad patterns. For every vertex, the abundance of each triad pattern is considered only in triads it participates in. We investigate systems of various fields and find that motifs are distributed highly heterogeneously. In particular we focus on the feed-forward loop motif which has been alleged to play a key role in biological networks.