Classification of transport backbones of complex networks

Area of Science:

• Network Science
• Statistical Physics
• Complex Systems

Background:

• Understanding transport properties is crucial for analyzing network behavior.
• Betweenness centrality (BC) is a key metric for network analysis.
• Scale-free (SF) networks exhibit unique structural properties.

Purpose of the Study:

• To investigate transport properties in random and SF networks.
• To analyze the betweenness centrality distribution in minimum spanning trees (MSTs) and infinite incipient percolation clusters (IIPCs).
• To determine the scaling exponents (δ) governing BC distribution in these network structures.

Main Methods:

• Analysis of betweenness centrality (BC) distribution P(B).
• Examination of MSTs and IIPCs within random and SF networks.
• Mathematical derivation relating BC to tree branch size.

Main Results:

• P(B) in MSTs follows a power-law scaling P(B)∼B(-δ).
• Two distinct scaling exponents were found for MSTs: δ≃1.6 (near-critical trees) and δ≃2.0 (supercritical trees).
• A scaling exponent of δ=1.5 was observed in IIPCs, consistent with their critical nature.

Conclusions:

• The scaling behavior of BC in MSTs is dependent on the network's criticality.
• The findings for MSTs provide a basis for understanding why δ≥2 in original networks.
• IIPCs exhibit a distinct, critical scaling behavior.