Maximizing influence propagation in networks with community structure

We consider the algorithmic problem of selecting a set of target nodes that cause the biggest activation cascade in a network. In case when the activation process obeys the diminishing return property, a simple hill-climbing selection mechanism has been shown to achieve a provably good performance. Here we study models of influence propagation that exhibit critical behavior and where the property of diminishing returns does not hold. We demonstrate that in such systems the structural properties of networks can play a significant role. We focus on networks with two loosely coupled communities and show that the double-critical behavior of activation spreading in such systems has significant implications for the targeting strategies. In particular, we show that simple strategies that work well for homogenous networks can be overly suboptimal and suggest simple modification for improving the performance by taking into account the community structure.