Interest Clustering Coefficient: a New Metric for Directed Networks like Twitter

TL;DR

This paper introduces the interest clustering coefficient, a new metric for directed social graphs like Twitter, capturing informational clustering better than existing metrics, demonstrated on a large-scale Twitter dataset.

Contribution

The paper proposes a novel interest clustering coefficient for directed graphs and applies it to a massive Twitter snapshot, revealing its effectiveness over traditional metrics.

Findings

Interest clustering coefficient exceeds traditional directed clustering metrics.

The new metric better captures informational clustering in directed social graphs.

Large-scale analysis on Twitter shows the metric's practical relevance.

Abstract

We study here the clustering of directed social graphs. The clustering coefficient has been introduced to capture the social phenomena that a friend of a friend tends to be my friend. This metric has been widely studied and has shown to be of great interest to describe the characteristics of a social graph. In fact, the clustering coefficient is adapted for a graph in which the links are undirected, such as friendship links (Facebook) or professional links (LinkedIn). For a graph in which links are directed from a source of information to a consumer of information, it is no more adequate. We show that former studies have missed much of the information contained in the directed part of such graphs. We thus introduce a new metric to measure the clustering of a directed social graph with interest links, namely the interest clustering coefficient. We compute it (exactly and using sampling methods) on a very large social graph, a Twitter snapshot with 505 million users and 23 billion links. We additionally provide the values of the formerly introduced directed and undirected metrics, a first on such a large snapshot. We exhibit that the interest clustering coefficient is larger than classic directed clustering coefficients introduced in the literature. This shows the relevancy of the metric to capture the informational aspects of directed graphs.