Clustering determines the dynamics of complex contagions in multiplex networks

摘要

We present the mathematical analysis of generalized complex contagions in a class of clustered multiplexnetworks. The model is intended to understand spread of influence, or any other spreading process implying athreshold dynamics, in setups of interconnected networks with significant clustering. The contagion is assumed tobe general enough to account for a content-dependent linear threshold model, where each link type has a differentweight (for spreading influence) that may depend on the content (e.g., product, rumor, political view) that is beingspread. Using the generating functions formalism, we determine the conditions, probability, and expected size ofthe emergent global cascades. This analysis provides a generalization of previous approaches and is especiallyuseful in problems related to spreading and percolation. The results present nontrivial dependencies between theclustering coefficient of the networks and its average degree. In particular, several phase transitions are shown tooccur depending on these descriptors. Generally speaking, our findings reveal that increasing clustering decreasesthe probability of having global cascades and their size, however, this tendency changes with the average degree.There exists a certain average degree from which on clustering favors the probability and size of the contagion.By comparing the dynamics of complex contagions over multiplex networks and their monoplex projections, wedemonstrate that ignoring link types and aggregating network layers may lead to inaccurate conclusions aboutcontagion dynamics, particularly when the correlation of degrees between layers is high.