Methods to Determine Node Centrality and Clustering in Graphs with Uncertain Structure

TL;DR

This paper introduces probabilistic measures for node centrality and clustering in uncertain graphs, improving the analysis of dynamic and noisy networks beyond traditional discrete graph methods.

Contribution

It develops novel probabilistic network measures based on sampling and paths, addressing uncertainty in graph structures that traditional methods cannot handle.

Findings

More accurate capture of salient effects in real-world networks

Enhanced understanding of graph structure under uncertainty

Robustness to local noise in network analysis

Abstract

Much of the past work in network analysis has focused on analyzing discrete graphs, where binary edges represent the "presence" or "absence" of a relationship. Since traditional network measures (e.g., betweenness centrality) utilize a discrete link structure, complex systems must be transformed to this representation in order to investigate network properties. However, in many domains there may be uncertainty about the relationship structure and any uncertainty information would be lost in translation to a discrete representation. Uncertainty may arise in domains where there is moderating link information that cannot be easily observed, i.e., links become inactive over time but may not be dropped or observed links may not always corresponds to a valid relationship. In order to represent and reason with these types of uncertainty, we move beyond the discrete graph framework and develop social network measures based on a probabilistic graph representation. More specifically, we develop measures of path length, betweenness centrality, and clustering coefficient---one set based on sampling and one based on probabilistic paths. We evaluate our methods on three real-world networks from Enron, Facebook, and DBLP, showing that our proposed methods more accurately capture salient effects without being susceptible to local noise, and that the resulting analysis produces a better understanding of the graph structure and the uncertainty resulting from its change over time.