The collective organization of living organisms in heterogeneous environments is a central issue in population dynamics. In particular, it is relevant to know how fragmented structures arise and, mainly, if in the long term the population will survive or become extinct. We address these problems from the perspective of single species populations.
The non-backtracking matrix and its eigenvalues have many applications in network science and graph mining, such as node and edge centrality, community detection, length spectrum theory, graph distance, and epidemic and percolation thresholds. Moreover, in network epidemiology, the reciprocal of the largest eigenvalue of the non-backtracking matrix is a good approximation for the epidemic threshold of certain network dynamics. In this work, we develop techniques that identify which nodes have the largest impact on the leading non-backtracking eigenvalue.
During the early months of the COVID-19 pandemic, many nations around the world developed smartphone-based solutions to mitigate the disease. Among these solutions have been contact tracing technologies. These smartphone based contact tracing systems use data about phone proximity, such as Bluetooth connectivity data, to track when smartphone users have been in contact for a significant duration. This data is used to signal to users when they may have been exposed to a person who has tested positive for COVID-19.
Understanding the role of individual nodes is a key challenge in the study of spreading processes on complex networks. In this work we propose a novel metric, the reachability-heterogeneity (RH), to quantify the vulnerability of each node with respect to a spreading process on a network.