  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.
