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The robustness of a network is depending on the type of attack we are considering. In this paper we focus on the spread of viruses on networks. It is common practice to use the epidemic threshold as a measure for robustness. Because the epidemic threshold is inversely proportional to the largest eigenvalue of the adjacency matrix, it seems easy to compare the robustness of two networks. We will show in this paper that the comparison of the robustness with respect to virus spread for two networks actually depends on the value of the effective spreading rate tau. For this reason we propose a new metric, the viral conductance, which takes into account the complete range of values tau can obtain. In this paper we determine the viral conductance of regular graphs, complete bi-partite graphs and a number of realistic networks.
An error is spotted in the statement of Theorem~1.3 of our published article titled On oriented cliques with respect to push operation (Discrete Applied Mathematics 2017). The theorem provided an exhaustive list of 16 minimal (up to spanning subgraph
This paper describes a mathematical model for the spread of a virus through an isolated population of a given size. The model uses three, color-coded components, called molecules (red for infected and still contagious; green for infected, but no long
We investigate a special case of hereditary property in graphs, referred to as {em robustness}. A property (or structure) is called robust in a graph $G$ if it is inherited by all the connected spanning subgraphs of $G$. We motivate this definition u
In the theory of operator quantum error correction (OQEC), the notion of correctability is defined under the assumption that states are perfectly initialized inside a particular subspace, a factor of which (a subsystem) contains the protected informa
The paper studies multi-competitive continuous-time epidemic processes in the presence of a shared resource. We consider the setting where multiple viruses are simultaneously prevalent in the population, and the spread occurs due to not only individu