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Community detectability and structural balance dynamics in signed networks.

Megan Morrison1, Michael Gabbay2

  • 1Department of Applied Mathematics, University of Washington, Washington 98115, USA.

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Summary
This summary is machine-generated.

We analyzed signed networks and community structure using spectral analysis and structural balance dynamics. Our findings reveal transitions predicting cooperation and conflict outcomes in social networks.

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Area of Science:

  • Network Science
  • Sociophysics
  • Statistical Mechanics

Background:

  • Signed networks are crucial for understanding social dynamics, with structural balance theory explaining cooperation and conflict.
  • Community structure influences network evolution and stability.
  • Spectral properties of networks offer insights into their underlying organization.

Purpose of the Study:

  • To investigate the spectral properties of signed networks with community structure.
  • To analyze the evolution of these networks under structural balance dynamics.
  • To identify spectral transitions that predict network outcomes.

Main Methods:

  • Generated signed networks using a stochastic block model with two equal-sized communities.
  • Analyzed the adjacency matrix spectra to identify detectability and sociality transitions.
  • Simulated structural balance dynamics on these networks to observe emergent regimes.

Main Results:

  • Detected transitions in network spectra related to community structure and average tie value.
  • Derived analytical expressions for eigenvalues and transition boundaries, validated by numerical results.
  • Identified three distinct outcome regimes: two-faction hostile (correlated or uncorrelated) and single-faction harmonious.

Conclusions:

  • Spectral transitions, specifically detectability and sociality, accurately predict the boundaries between different network states.
  • These findings offer insights into the interplay of cooperation and conflict in social systems with distinct identities.