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Related Experiment Video

Updated: Mar 24, 2026

Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks

Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks

Published on: September 25, 2021

Correlation between weighted spectral distribution and average path length in evolving networks.

Bo Jiao¹, Jianmai Shi², Xiaoqun Wu³

¹Luoyang Electronic Equipment Test Center, Luoyang 471003, China.

Chaos (Woodbury, N.Y.)

|March 3, 2016

Summary

The weighted spectral distribution (WSD) metric scales sublinearly with network size across various degree distributions. Its ratio to network size effectively indicates average path length in evolving networks.

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Area of Science:

Network Science
Graph Theory
Data Analysis

Background:

The weighted spectral distribution (WSD) is a metric derived from the normalized Laplacian spectrum.
Understanding network properties requires analyzing metrics like WSD across different network structures.

Purpose of the Study:

To rigorously analyze the scaling feature of the WSD metric.
To investigate the correlation between WSD and average path length in both static and evolving networks.
To explore the relationship between WSD and network size and degree distributions.

Main Methods:

Analysis of synchronic random graphs with varying degree distributions (Gaussian, exponential, power-law).
Development of a deterministic model for diachronic graphs to study evolving networks.
Numerical analysis using simulated and real-world evolving network data.

Main Results:

The WSD metric exhibits sublinear growth with increasing network size.
This scaling feature is consistent across networks with different degree distributions.
A correlation was established between the WSD's slope coefficient and average path length.
The ratio of WSD to network size serves as a reliable indicator of average path length.

Conclusions:

The WSD metric provides insights into network structure and evolution.
The ratio of WSD to network size is a valuable indicator for estimating average path length.
The study clarifies similarities and differences between synchronic and diachronic random graph models.