Tighter spectral bounds for the cut size, based on Laplacian eigenvectors

The cut-set ∂V in a graph is defined as the set of all links between a set of nodes V and all other nodes in that graph. Finding bounds for the size of a cut-set |∂V| is an important problem, and is related to mixing times, connectedness and spreading processes on networks. A standard way to bound the number of links in a cut-set |∂V| relies...

Structure and dynamics of complex networks: Network epidemics and a geometric robustness measure

As new technologies continue to find their way into everyday life, the world becomes more and more connected. Airplanes and other means of transportation provide global connections in the physical world, while the omnipresence of the Internet means that information is shared around the globe, easier than ever before. But not only these man-made...