Longitudinal Modularity, a Modularity for Link Streams

Temporal networks are commonly used to model real-life phenomena. When these phenomena represent interactions and are captured at a fine-grained temporal resolution, they are modeled as link streams. Community detection is an essential network analysis task. Although many methods exist for static networks, and some methods have been developed for temporal networks represented as sequences of snapshots, few works can handle link streams. This article introduces the first adaptation of the well-known Modularity quality function to link streams. Unlike existing methods, it is independent of the time scale of analysis. After introducing the quality function, and its relation to existing static and dynamic definitions of Modularity, we show experimentally its relevance for dynamic community evaluation.

Temporal and Geographical Analysis of Real Economic Activities in the Bitcoin Blockchain

We study the real economic activity in the Bitcoin blockchain that involves transactions from/to retail users rather than between organizations such as marketplaces, exchanges, or other services. We first introduce a heuristic method to classify Bitcoin players into three main categories: Frequent Receivers (FR), Neighbors of FR, and Others. We show that most real transactions involve Frequent Receivers, representing a small fraction of the total value exchanged according to the blockchain, but a significant fraction of all payments, raising concerns about the centralization of the Bitcoin ecosystem. We also conduct a weekly pattern analysis of activity, providing insights into the geographical location of Bitcoin users and allowing us to quantify the bias of a well-known dataset for actor identification.

Evaluating Community Detection Algorithms for Progressively Evolving Graphs

Many algorithms have been proposed in the last ten years for the discovery of dynamic communities. However, these methods are seldom compared between themselves. In this article, we propose a generator of dynamic graphs with planted evolving community structure, as a benchmark to compare and evaluate such algorithms. Unlike previously proposed benchmarks, it is able to specify any desired evolving community structure through a descriptive language, and then to generate the corresponding progressively evolving network. We empirically evaluate six existing algorithms for dynamic community detection in terms of instantaneous and longitudinal similarity with the planted ground truth, smoothness of dynamic partitions, and scalability. We notably observe different types of weaknesses depending on their approach to ensure smoothness, namely Glitches, Oversimplification and Identity loss. Although no method arises as a clear winner, we observe clear differences between methods, and we identified the fastest, those yielding the most smoothed or the most accurate solutions at each step.