The role of local topological information in viral information spreading

The intricate structure of many large-scale networked systems has attracted the attention of the scientific community, leading to many results attempting to explain the relationship between a network's structural features and the performance of spreading processes taking place in the network. A common approach to study this relationship is the usage of random networks in which structural properties of interest are prescribed. Although very common, this approach presents two major flaws. First, traditional random networks only allow to study the effect of very simple structural properties, such as degree distributions, on spreading processes. Second, random networks indirectly induce structural properties that are not directly controlled in the random model and can influence the behavior of spreading processes. In this work, we propose an alternative approach to overcome these limitations. In our approach, we use algebraic graph theory and convex optimization to study how structural properties constrain the behavior of spreading processes in the network. Based on our results, we analytically study the effect of a collection of relevant structural properties in the behavior of spreading processes in large-scale networks. We illustrate our approach with nontrivial numerical simulations using real data from an online social network.