On the submodularity of influence in social networks

We prove and extend a conjecture of Kempe, Kleinberg, and Tardos (KKT) on the spread of influence in social networks. A social network can be represented by a directed graph where the nodes are individuals and the edges indicate a form of social relationship. A simple way to model the diffusion of ideas, innovative behavior, or "word-of-mouth" effects on such a graph is to consider an increasing process of "infected" (or active) nodes: each node becomes infected once an activation function of the set of its infected neighbors crosses a certain threshold value. Such a model was introduced by KKT in [7, 8] where the authors also impose several natural assumptions: the threshold values are (uniformly) random to account for our lack of knowledge of the true values; and the activation functions are monotone and submodular, i.e. have "diminishing returns." The monotonicity condition indicates that a node is more likely to become active if more of its neighbors ...

• Type: Conference
• Year: 2007
• Where: STOC
• Authors: Elchanan Mossel, Sébastien Roch
• Keywords: Active Nodes, Alfred Sloan Fellowship, Algorithms, Natural Computational Interest, STOC 2007