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Abstract
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.
Highlights
Multi-layer interdependent networks (M-IDNs) are systems composed of more than one network with edges between them to form an interconnected environment
We propose a modified version of the threshold-based phenomena propagation model that was initially proposed in (Khamfroush et al 2016) for a general interdependent network and a single phenomenon, as a mathematical model to quantify the impact of different strategies for selecting initial spreaders for phenomena propagation in an M-IDN system
For the two networks composing the M-IDN topology for our study, we introduce two different threshold functions: kaa(i) ∈ (0, 1] for i ∈ A, and kbb(i) ∈
Summary
Multi-layer interdependent networks (M-IDNs) are systems composed of more than one network with edges between them to form an interconnected environment. We have seen an exponential growth in the development and deployment of these systems This growth is largely due Khamfroush et al Applied Network Science (2019) 4:40 to the increasing use of more technologies interfacing with one another — such as the Internet of Things. The main reason for such wide-spread damage was the interdependency between the supervisory control and data acquisition (SCADA) system controlling the nuclear enrichment plants and the enrichment plants. This huge impact would likely not have been possible without the interdependency between the cyber (controller) component and the physical component’s performance
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