A Gauge-Invariant Clustering Coefficient for Complex-Weighted Bipartite Networks
This work defines a new clustering coefficient for bipartite networks with complex edge weights, which are common in quantum and photonic systems where phases matter. The new coefficient reduces to the classical measure when phases are zero, becomes negative when alternative routes interfere destructively, and separates into topological and phase components. This shows that phase disorder increases the coherent distance while leaving hop-count distances unchanged.