Uncovering Complex Overlapping Pattern of Communities in Large-scale Social Networks
Elvis H. W. Xu, Pak Ming Hui

TL;DR
This paper introduces a scalable method called PCMA for detecting overlapping communities in large social networks and provides an in-depth analysis revealing complex community overlaps and their structural properties.
Contribution
The paper presents a new linear-complexity algorithm for large-scale overlapping community detection and offers detailed empirical insights into community structures in social networks.
Findings
Communities often overlap significantly and have more outbound edges than internal edges.
Most vertices are multi-membership, existing at core or peripheral positions.
A dense network of communities accounts for nearly half of the entire network.
Abstract
The conventional notion of community that favors a high ratio of internal edges to outbound edges becomes invalid when each vertex participates in multiple communities. Such a behavior is commonplace in social networks. The significant overlaps among communities make most existing community detection algorithms ineffective. The lack of effective and efficient tools resulted in very few empirical studies on large-scale detection and analyses of overlapping community structure in real social networks. We developed recently a scalable and accurate method called the Partial Community Merger Algorithm (PCMA) with linear complexity and demonstrated its effectiveness by analyzing two online social networks, Sina Weibo and Friendster, with 79.4 and 65.6 million vertices, respectively. Here, we report in-depth analyses of the 2.9 million communities detected by PCMA to uncover their complex…
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