Structural Sign Herdability in Temporal Networks: A Sufficient Condition via pi p-Graphs
The study investigates structural sign (SS) herdability in temporal networks with fixed switching sequences. It introduces a novel graph concept, the $\pi$-graph, which is a spanning subgraph of the union multigraph that ensures all temporal walks from the leader have consistent path signs. The existence of this specific $\pi_p$-graph is proven to be sufficient to guarantee SS herdability.