Fast Optimized Community Significance (FOCS)

Fast Optimized Community Significance (FOCS) assesses the statistical significance of detected communities in networks by generalizing null models and applying a significance scoring algorithm to unipartite and bipartite graphs.

Key Features:

• Scalability: Scales to large networks to enable analysis of extensive bipartite and unipartite graphs.
• Graph agnosticism: Operates on both unipartite and bipartite network structures without being limited to a single graph type.
• Numerical stability: Implements algorithmic choices to reduce numerical instability during computations on large datasets.
• Balanced detection: Balances detection power with minimization of false positives when assessing community significance.
• Bipartite extension: Extends existing community significance testing methods specifically to bipartite graphs.
• Significance scoring algorithm: Computes per-community significance scores to quantify deviation from null-model expectations.
• Generalized null models and statistical tests: Generalizes existing null models and statistical tests for application to bipartite networks.

Scientific Applications:

• Network community analysis: Detects and quantifies statistically significant communities in diverse network datasets, including both unipartite and bipartite graphs.
• Unsupervised learning, feature discovery, and anomaly detection: Validates whether communities used as features or clusters exhibit significance beyond random graph expectations.
• IMDB bipartite graph analysis: Applied to an IMDB-derived bipartite actor/director graph to identify significant actor/director collaborations on serial cinematic projects, with significance scores that correlated with collaborative patterns.

Methodology:

Generalizes null models and statistical tests to bipartite graphs and computes community-level significance using a dedicated significance scoring algorithm.