Multi-dimensional Threshold model with correlation: emergence of global cascades

Study of complex contagions over networks has been receiving increasing attention across many scientific domains. Especially, linear threshold models are widely studied due to the ability to capture the mechanism that multiple sources of exposure are required for nodes in the network to take action. Most related works on influence propagation only concentrate on a single content spreading over networks. However, complex contagions usually involve multiple correlated contents spreading simultaneously and show significant implications in many real life systems. In this work, we propose the multi-dimensional threshold model, as an extension of the classical linear threshold model to incorporate multiple correlated contents spreading simultaneously over networks. We also provide analytical results that accurately predict probability of emergence of global cascades for correlated contents. Our analytical results reveal the interplay between the underlying network structure, content correlation on the spreading processes. Thus they might help with analysis, prediction and control strategies.