Stars, holes, or paths across your Facebook friends: A graphlet-based characterization of many networks

Abstract

Network science gathers methods coming from various disciplines which sometimes hardly cross the boundaries between these disciplines. Widely used in molecular biology in the study of protein interaction networks, the enumeration, in a network, of all possible subgraphs of a limited size (usually around four or five nodes), often called graphlets, can only be found in a few works dealing with social networks. In the present work, we apply this approach to an original corpus of about 10,000 non-overlapping Facebook ego networks gathered from voluntary participants by a survey application. To deal with so many similar networks, we adapt the relative graphlet frequency to a measure that we call graphlet representativity, which we show to be more effective to classify random networks having slight structural differences. From our data, we produce two clusterings, one of graphlets (paths, star-like, holes, light triangles, and dense), one of networks. The latter is presented with a visualization scheme using our representativity measure. We describe the distinct structural characteristics of the five clusters of Facebook ego networks so obtained and discuss the empirical differences between results obtained with 4-node and 5-node graphlets. We also provide suggestions of follow-ups of this work, both in sociology and in network science.

Tailored vertex ordering for faster triangle listing in large graphs

“…Software and hardware. We release a uniform open-source implementation 5 of A++ and A+-algorithms, as well as the different ordering strategies that we discussed. Our implementation allows to run either algorithm in parallel, which is possible because each iteration of the main loop is independent from the others.…”

“…Small connected subgraphs are key to identify families of real-world networks [19] and are used for descriptive or predictive purposes in various fields such as biology [27,21], sociology [7,5] and engineering [29]. In particular, listing elementary patterns such as triangles is a stepping stone to analyze the structure of networks and their evolution [15,26].…”

Investigating scientific mobility in co-authorship networks using multilayer temporal motifs

“…Due to the difficulty of developing an underlying null hypothesis that correctly and exhaustively captures the basic mechanics of coauthorship networks (Artzy-Randrup et al, 2004), we do not compare our motif count results with a null model but instead compare them with one another. Similar to the graphlet representativity measure by Charbey & Prieur (2019), we compute the difference between the relative frequency in one network and the relative "global", i.e., average, frequency. We do this not for individual motif configurations but for the motif categories.…”

VAST 2020 Contest Challenge: GraphMatchMaker—Visual Analytics for Graph Comparison and Matching

“…In a typical graphlet analysis, the frequency of each graphlet is computed and normalized, providing a distribution of the graphlets which occur in a graph. Graphlet frequencies can be computed on an entire graph or around a specific node (ego networks) to compare the frequencies of each node [6]. This is mostly done by computing similarity measures that grasp the differences between the distributions of the graphlet frequencies [7].…”