Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Search research articles

Related Experiment Videos

L -percolations of complex networks.

Luciano da Fontoura Costa¹

¹Institute of Physics of São Carlos, University of São Paulo, São Carlos, SP, P.O. Box 369, 13560-970 Brazil. luciano@if.sc.usp.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 17, 2004

Summary

Complex networks exhibit L-percolations, phase transitions that enhance connectivity and community detection. For L=3, networks percolate before L=2, revealing Eulerian giant clusters.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Interrelating neuronal morphology by coincidence similarity networks.

Journal of theoretical biology·2025

Same author

Correlations between structure and random walk dynamics in directed complex networks.

Applied physics letters·2020

Same author

Comparison of Different Spike Train Synchrony Measures Regarding Their Robustness to Erroneous Data From Bicuculline-Induced Epileptiform Activity.

Neural computation·2020

Same author

Morphological Neuron Classification Based on Dendritic Tree Hierarchy.

Neuroinformatics·2018

Same author

Gene regulatory and signaling networks exhibit distinct topological distributions of motifs.

Physical review. E·2018

Same author

Effects of threshold on the topology of gene co-expression networks.

Molecular bioSystems·2017

Area of Science:

Network Science
Complex Systems Analysis
Statistical Physics

Background:

Complex networks are fundamental to understanding systems across various domains.
Identifying community structures and connectivity patterns is crucial for network analysis.
Existing methods may not fully capture the nuanced connectivity of evolving networks.

Purpose of the Study:

To introduce and analyze the concept of L-conditional network expansions.
To investigate the phenomenon of L-percolations in evolving complex networks.
To determine the conditions under which L-percolations occur and their impact on network structure.

Main Methods:

Definition of L-paths and L-conditional network expansions.
Intersection of original networks with their L-expansions to form conditional L-expansions.
Analytical and experimental investigations of network evolution for L=2 and L=3.
Analysis of phase transitions and the formation of Eulerian giant clusters.

Main Results:

L-conditional expansions act as filters, enhancing network connectivity.
Evolving complex networks with a fixed number of nodes undergo successive L-percolations.
These percolations lead to the formation of Eulerian giant clusters.
Critical percolation values depend on network size, with L=3 percolation preceding L=2.

Conclusions:

L-conditional expansions provide a novel method for filtering and analyzing network connectivity.
The study demonstrates successive phase transitions (L-percolations) in evolving networks.
The findings offer insights into community detection and the structural evolution of complex networks.

Related Experiment Videos