Where to cut to delay a pandemic with minimum disruption? mathematical analysis based on the SIS model

We consider the problem of modifying a network topology in such a way as to delay the propagation of a disease with minimal disruption of the network capacity to reroute goods/items/passengers. We find an approximate solution to the Susceptible-Infected-Susceptible (SIS) model, which constitutes an upper bound to its exact solution. This upper bound allows direct structure-epidemic dynamic relations via the total communicability function. Using this approach we propose a strategy to remove edges in a network that significantly delays the propagation of a disease across the network with minimal disruption of its capacity to deliver goods/items/passengers. We apply this strategy to the analysis of the UK airport transportation network weighted by the number of passengers transported in 2003. We find that the removal of all flights connecting four origin-destination pairs in the UK delays the propagation of a disease by more than 300%, with a minimal deterioration of the transportation capacity of this network. These time delays in the propagation of a disease represent an important non-pharmaceutical intervention to confront an epidemic, allowing for better preparations of the health systems, while keeping the economy moving with minimal disruptions.

Network bipartitioning in the anti-communicability euclidean space

We define the anti-communicability function for the nodes of a simple graph as the nondiagonal entries of exp (−A). We prove that it induces an embedding of the nodes into a Euclidean space. The anti-communicability angle is then defined as the angle spanned by the position vectors of the corresponding nodes in the anti-communicability Euclidean space. We prove analytically that in a given k-partite graph, the anti-communicability angle is larger than 90° for every pair of nodes in different partitions and smaller than 90° for those in the same partition. This angle is then used as a similarity metric to detect the “best” k-partitions in networks where certain level of edge frustration exists. We apply this method to detect the “best” k-partitions in 15 real-world networks, finding partitions with a very low level of “edge frustration”. Most of these partitions correspond to bipartitions but tri- and pentapartite structures of real-world networks are also reported.

Parametric definition of the influence of a paper in a citation network using communicability functions

Communicability functions quantify the flow of information between two nodes of a network. In this work, we use them to explore the concept of the influence of a paper in a citation network. These functions depend on a parameter. By varying the parameter in a continuous way we explore different definitions of influence. We study six citation networks, three from physics and three from computer science. As a benchmark, we compare our results against two frequently used measures: the number of citations of a paper and the PageRank algorithm. We show that the ranking of the articles in a network can be varied from being equivalent to the ranking obtained from the number of citations to a behaviour tending to the eigenvector centrality, these limits correspond to small and large values of the communicability-function parameter, respectively. At an intermediate value of the parameter a PageRank-like behaviour is recovered. As a test case, we apply communicability functions to two sets of articles, where at least one author of each paper was awarded a Nobel Prize for the research presented in the corresponding article.