Power network uniqueness and synchronization stability from a higher-order structure perspective

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 maintain a high level of synchronization stability at a low construction cost.