Moment-Based Analysis of Spreading Processes from Network Structural Information

Victor M. Preciado∗ and Ali Jadbabaie† Department of Electrical and Systems Engineering University of Pennsylvania, Philadelphia, PA 19104‡ Abstract 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 network structural properties and dynamical performance. A common approach to study this relationship is the usage of synthetic network models in which the researcher can prescribe structural properties of interest, such as degree distributions. Researchers then estimate performance metrics of the synthetic network and study the effect of structural variations in these metrics. Although very common, this approach present a major flaw: Synthetic network models implicitly induce structural properties that are not directly controlled and can be relevant to the network dynamical performance. Therefore, it is difficult to isolate the role of a particular network property in the dynamical performance using synthetic networks. In this paper, we propose an alternative approach to overcome this flaw. Furthermore, our analysis unveils the set of structural properties that are most relevant to the network dynamical performance. We illustrate our approach by studying the dynamics of viral spreading processes in complex networks. Our analysis builds on algebraic graph theory and convex optimization to study how network structural properties constrain the behavior of viral spreading. We illustrate our approach with nontrivial numerical simulations in an online social network.