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Clique densification in networks.

Haochen Pi1, Keith Burghardt2, Allon G Percus2,3

  • 1Department of Computer Science, University of Southern California, Los Angeles, California 90007, USA.

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Summary
This summary is machine-generated.

Real-world networks exhibit superlinear scaling laws for higher-order cliques, with exponents increasing with clique size. A new local preferential attachment model explains this network growth and redundancy.

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Area of Science:

  • Network Science
  • Graph Theory
  • Complex Systems

Background:

  • Real-world networks are dynamic, with increasing interest in network growth and densification.
  • Scaling laws of higher-order cliques are crucial for understanding network clustering and redundancy but are less studied.

Purpose of the Study:

  • To investigate the scaling laws of higher-order cliques in empirical networks.
  • To propose and validate a new model for network growth that accounts for clique scaling.

Main Methods:

  • Analysis of several empirical networks (e.g., email, Wikipedia interactions).
  • Examination of how clique size scales with network size.
  • Development and comparison with a proposed local preferential attachment model.

Main Results:

  • Empirical networks demonstrate superlinear scaling laws for higher-order cliques.
  • The exponents of these scaling laws increase with clique size, contradicting previous models.
  • Results align with the proposed local preferential attachment model.

Conclusions:

  • Higher-order clique growth follows distinct superlinear scaling laws in real-world networks.
  • The local preferential attachment model provides a framework for understanding clique growth and network redundancy.
  • Findings offer insights into the mechanisms driving network evolution and structural properties.