Counting Balanced Triangles on Social Networks With Uncertain Edge Signs

TL;DR

This paper develops methods for counting and enumerating balanced and unbalanced triangles in social networks where edge signs are uncertain, using probabilistic models and sampling techniques to improve efficiency and accuracy.

Contribution

It introduces novel probabilistic approaches for triangle counting in uncertain signed networks, including exact, improved, and sampling-based methods, with significant efficiency gains.

Findings

Improved exact counting method reduces search space.

Sampling approaches achieve over 100x faster queries.

Methods effectively analyze real-world uncertain networks.

Abstract

On signed social networks, balanced and unbalanced triangles are a critical motif due to their role as the foundations of Structural Balance Theory. The uses for these motifs have been extensively explored in networks with known edge signs, however in the real-world graphs with ground-truth signs are near non-existent, particularly on a large-scale. In reality, edge signs are inferred via various techniques with differing levels of confidence, meaning the edge signs on these graphs should be modelled with a probability value. In this work, we adapt balanced and unbalanced triangles to a setting with uncertain edge signs and explore the problems of triangle counting and enumeration. We provide a baseline and improved method (leveraging the inherent information provided by the edge probabilities in order to reduce the search space) for fast exact counting and enumeration. We also explore approximate solutions for counting via different sampling approaches, including leveraging insights from our improved exact solution to significantly reduce the runtime of each sample resulting in upwards of two magnitudes more queries executed per second. We evaluate the efficiency of all our solutions as well as examine the effectiveness of our sampling approaches on real-world topological networks with a variety of probability distributions.