The complexity of heterogeneity in real-world networks

Many real-world phenomena are characterized by complex structures. Modeling and detecting these architectures is of paramount importance to understand the dynamics of the considered systems and to consciously intervene on them. The COVID-19 pandemic is, in this sense, a telling example. One common feature of these complex structures is the heterogeneity of the node connectivity of the underlying network. This heterogeneity is one of the main culprits of the ongoing pandemic. In this thesis, we introduce a method capable of uncovering complex networks’ heterogeneous structures when finite-size effects hide the latter. Larger heterogeneity in the network structure leads to a smaller epidemic threshold. It is not a coincidence that policymakers worldwide are trying to reduce this heterogeneity (employing lockdowns and other less restrictive measurements) to stop the spread of the virus. We show that a macro-quarantine followed by a micro-quarantine can help in this direction. For this scope, we introduce an algorithm that is able to track super-spreaders. Notably, the same algorithm can be used to define an optimized strategy for vaccinations. Similarly to a virus, information continuously spreads on social networks. By combining Machine Learning and network theory techniques, we develop an algorithm able to discover what “social users” think about a particular topic—a sort of social listener, an AI alternative to traditional polls.