Influence spread in two-layer interdependent networks: designed single-layer or random two-layer initial spreaders?

Influence spread in multi-layer interdependent networks (M-IDN) has been studied in the last few years; however, prior works mostly focused on the spread that is initiated in a single layer of an M-IDN. In real world scenarios, influence spread can happen concurrently among many or all components making up the topology of an M-IDN. This paper investigates the effectiveness of different influence spread strategies in M-IDNs by providing a comprehensive analysis of the time evolution of influence propagation given different initial spreader strategies. For this study we consider a two-layer interdependent network and a general probabilistic threshold influence spread model to evaluate the evolution of influence spread over time. For a given coupling scenario, we tested multiple interdependent topologies, composed of layers A and B, against four cases of initial spreader selection: (1) random initial spreaders in A, (2) random initial spreaders in both A and B, (3) targeted initial spreaders using degree centrality in A, and (4) targeted initial spreaders using degree centrality in both A and B. Our results indicate that the effectiveness of influence spread highly depends on network topologies, the way they are coupled, and our knowledge of the network structure — thus an initial spread starting in only A can be as effective as initial spread starting in both A and B concurrently. Similarly, random initial spread in multiple layers of an interdependent system can be more severe than a comparable initial spread in a single layer. Our results can be easily extended to different types of event propagation in multi-layer interdependent networks such as information/misinformation propagation in online social networks, disease propagation in offline social networks, and failure/attack propagation in cyber-physical systems.