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A network function-based definition of communities in complex networks.

Sanjeev Chauhan1, Michelle Girvan, Edward Ott

  • 1Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA.

Chaos (Woodbury, N.Y.)
|October 2, 2012
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Summary
This summary is machine-generated.

This study introduces a new, function-driven method for network community detection. It optimizes network communities by maximizing eigenvalues, enhancing synchronization and resilience, and compares it to the standard modularity approach.

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Area of Science:

  • Network Science
  • Complex Systems
  • Mathematical Biology

Background:

  • Traditional network community detection often overlooks functional network performance.
  • Network function, such as synchronization and resilience, is frequently influenced by network structure and dynamics.
  • The largest eigenvalue of a network's adjacency matrix is a key indicator for synchronization and percolation thresholds.

Purpose of the Study:

  • To propose and evaluate an alternative definition of network community structure that is functionally motivated.
  • To develop a method for community detection that maximizes a function of the largest eigenvalues of subnetwork adjacency matrices.
  • To compare the performance of this function-based method against the traditional modularity approach.

Main Methods:

  • Defined network community structure based on intended system function, specifically synchronization and resilience.
  • Proposed a method to partition networks by maximizing a function of the largest eigenvalues of the resulting community adjacency matrices.
  • Compared the obtained functional partitions with partitions derived from the modularity approach across various network types.

Main Results:

  • The proposed function-based method effectively identifies communities that enhance network function.
  • In many cases, modularity-based partitions performed comparably to the function-based method in identifying functional communities.
  • Differences were observed between function-based and structure-based (modularity) community partitions across different network classes.

Conclusions:

  • A functionally motivated approach to network community detection offers a valuable alternative to structure-based methods.
  • Eigenvalue-based optimization can effectively guide community detection for enhanced network performance.
  • While modularity is a useful structural metric, incorporating functional considerations can lead to more targeted community identification.