Power Network Uniqueness and Synchronization Stability from a Higher-order Structure Perspective

TL;DR

This paper analyzes power networks using higher-order connectivity patterns, revealing a unique triad significance profile that differentiates them from other complex networks and relates to their stability and construction cost.

Contribution

It introduces a higher-order structural perspective to identify power networks through a unique triad significance profile and links this to their stability and cost trade-offs.

Findings

Power networks have a distinct triad significance profile compared to other networks.

Triadic closure significance correlates with construction cost and redundancy.

Power networks form a unique superfamily characterized by their TSP.

Abstract

Triadic subgraph analysis reveals the structural features in power networks based on higher-order connectivity patterns. Power networks have a unique triad significance profile (TSP) of the five unidirectional triadic subgraphs in comparison with the scale-free, small-world and random networks. Notably, the triadic closure has the highest significance in power networks. Thus, the unique TSP can serve as a structural identifier to differentiate power networks from other complex networks. Power networks form a network superfamily. Furthermore, synthetic power networks based on the random growth model grow up to be networks belonging to the superfamily with a fewer number of transmission lines. The significance of triadic closures strongly correlates with the construction cost measured by network redundancy. The trade off between the synchronization stability and the construction cost leads to the power network superfamily. The power network characterized by the unique TSP is the consequence of the trade-off essentially. The uniqueness of the power network superfamily tells an important fact that power networks.