Characterizing Attitudinal Network Graphs through Frustration Cloud

TL;DR

This paper introduces the frustration cloud, a new set of measures for analyzing attitudinal network graphs by considering all nearest balanced states, enabling better understanding of consensus, controversy, and influence in large signed networks.

Contribution

The paper proposes a novel framework extending balance measures to the entire set of nearest balanced states, along with scalable algorithms and new metrics for social network analysis.

Findings

Efficient algorithm for large networks with up to 80,000 vertices.

Frustration cloud improves community detection over spectral clustering.

New metrics identify influential and anomalous vertices.

Abstract

Attitudinal Network Graphs are signed graphs where edges capture an expressed opinion; two vertices connected by an edge can be agreeable (positive) or antagonistic (negative). A signed graph is called balanced if each of its cycles includes an even number of negative edges. Balance is often characterized by the frustration index or by finding a single convergent balanced state of network consensus. In this paper, we propose to expand the measures of consensus from a single balanced state associated with the frustration index to the set of nearest balanced states. We introduce the frustration cloud as a set of all nearest balanced states and use a graph-balancing algorithm to find all nearest balanced states in a deterministic way. Computational concerns are addressed by measuring consensus probabilistically, and we introduce new vertex and edge metrics to quantify status, agreement, and influence. We also introduce a new global measure of controversy for a given signed graph and show that vertex status is a zero-sum game in the signed network. We propose an efficient scalable algorithm for calculating frustration cloud-based measures in social network and survey data of up to 80,000 vertices and half-a-million edges. We also demonstrate the power of the proposed approach to provide discriminant features for community discovery when compared to spectral clustering and to automatically identify dominant vertices and anomalous decisions in the network.