Abstract

Cascade dynamics in networks have been studied using the linear threshold model (LTM) on single layer networks. In the LTM any node in the network becomes active when a sufficiently large fraction of its neighbors is active. In reality, nodes may be interconnected through more than one sensing, communication, or physical modality. To explore what can happen when spreading protocols distinguish these modalities, we define the LTM on multiplex networks, which have multiple layers, each representing interconnections for a different modality. For example, in the “OR” protocol, a node becomes active if a large enough set of its visible neighbors or a large enough set of its audible neighbors is active; whereas in the “AND” protocol, the node becomes active only if both active sets are sufficiently large. We design an algorithm to compute nodal cascade centrality, which measures a node’s influence on the cascade dynamics. We show how different protocols can be used to investigate heterogeneity in cascade dynamics, i.e., in mixed groups of individuals with responsive (OR) or conservative (AND) tendencies. Extensions to continuous-time dynamics will be discussed.