Communities and bottlenecks: trees and treelike networks have high modularity

Area of Science:

• Network Science
• Graph Theory
• Data Analysis

Background:

• Complex networks are often analyzed for their modular structure, comprising densely interconnected communities.
• Community detection is crucial across various scientific domains.
• Modularity is a popular metric for both discovering and quantifying community strength in networks.

Purpose of the Study:

• To investigate how modularity metrics evaluate different network topologies.
• To understand the assumptions and features considered by modularity functions.
• To analyze the modular structure of tree and tree-like networks.

Main Methods:

• Analysis of modularity values for tree and tree-like network topologies.
• Evaluation of popular community detection methods on model trees.
• Application to a genealogical dataset.
• Statistical testing of discovered communities.

Main Results:

• Trees and tree-like networks demonstrate unexpectedly high modularity values.
• The nonlocal null model used by modularity assigns high significance to sparse tree communities.
• Community detection methods applied to trees yield high modularity scores, often near maximum.
• Statistical tests confirm the significance of communities in trees, contrasting with sparse random graphs.

Conclusions:

• Modularity metrics may overestimate community structure in sparse networks like trees.
• The findings challenge the typical understanding of modularity and community detection.
• Further research is needed to refine community detection methods for sparse network topologies.