Impact and unification of alternative higher-order annihilation mechanisms

Determine how alternative higher-order annihilation mechanisms for rumor spreading on hypergraphs—such as group-level threshold-based annihilation versus node-level monitoring of neighbors—modify the dynamics of the threshold rumor model with hyperedge-activation contagion and degree-based annihilation; ascertain whether these mechanisms can be unified into a single common class and specify the criteria for such unification.

Background

The paper proposes a threshold-based rumor model on hypergraphs that couples group-activated contagion with a group-based annihilation mechanism inspired by Daley–Kendall’s principle that stifling occurs through interaction with informed individuals. Specifically, contagion activates an entire hyperedge once a fraction of its members are spreaders, and annihilation occurs when a spreader belongs to a sufficient fraction of activated hyperedges.

The authors note that in contexts with small hyperedge cardinalities, it may be more realistic for spreaders to track individual neighbors rather than entire groups, motivating the exploration of alternative annihilation mechanisms. Understanding how these variations affect the system’s behavior and whether they belong to a single shared class remains unresolved.