A Vector Threshold Model for the Simultaneous Spread of Correlated Influence

Most existing works modeling influence propagation assume that there is only one content spreading over networks. However, an influence propagation process could have multiple correlated contents spreading simultaneously and exhibiting positive (e.g., opinions on same-sex marriage and gun control) or negative (e.g., opinions on universal healthcare and tax-relief for the ``rich") correlation. In a nutshell, few researchers model an influence propagation with the simultaneous spread of multiple correlated contents. Thus,for this scenario, we first propose a new model, the vector threshold model. For this model, we analyze the expected size of global cascades and find the condition of the existence of global cascades. Then, we confirm the correctness of our analysis by numerical studies. Next, we discuss how the correlation among contents affects the expected size of global cascades. In particular, when the mean degree of nodes is at a low level, the competitive, independent, and cooperative relationships produce global cascades with similar size. Only when the mean degree is at a high level do we see significant differences between these relationships on the expected size of global cascades.