Laplace eigenvalues of graphs—a survey

TL;DR: It is shown that the largest eigenvalue of the probabilistic connectivity matrix can serve as a good measure of the quality of network connectivity.

TL;DR: It is shown that the dynamics of hub nodes can be very well approximated by a low-dimensional system for exponentially long time in the size of the network and that the system exhibit hyperbolic behaviour in this time window.

TL;DR: This thesis addresses several problems related to modeling and control of power systems in microgrids, and derives an improved swing model for synchronous generators which, compared to the swing equation, predicts better the behavior of the system, and yet it is easy to use.

TL;DR: This paper provides a stable algorithm for the distributed, indulgent derivation of the Fiedler vector which is applicable within dynamic networks and shows its robustness to topology changes.

TL;DR: In this article, the authors introduce algebraic graph theory and show that the spectrum of a graph can be modelled as a graph graph, and the spectrum can be represented as a set of connected spanning trees.

TL;DR: The Spectrum and the Group of Automorphisms as discussed by the authors have been used extensively in Graph Spectra Techniques in Graph Theory and Combinatory Applications in Chemistry an Physics. But they have not yet been applied to Graph Spectral Biblgraphy.

TL;DR: It is proved that the Shannon zero-error capacity of the pentagon is \sqrt{5} and a well-characterized, and in a sense easily computable, function is introduced which bounds the capacity from above and equals the capacity in a large number of cases.

TL;DR: In this paper, it is shown that lower bounds on separator sizes can be obtained in terms of the eigenvalues of the Laplacian matrix associated with a graph.