10 papers
Finding all cospectral mates over a number field
Alexander Van Werde
We investigate a notion of cospectrality for integer matrices that is parameterized by algebraic number fields. Given a number field and a symmetric integer matrix, we wonder when…
Spectral graph clustering with inhomogeneous latent geometry
Konstantin Avrachenkov, Lucas S. Sibemberg, Alexander Van Werde
We study spectral clustering in the presence of a confounding latent geometry. The leading eigenvectors may then be dominated by the latent geometry rather than by the communities.…
Detection and Evaluation of Clusters within Sequential Data
Alexander Van Werde, Albert Senen-Cerda, Gianluca Kosmella +1
Sequential data is ubiquitous -- it is routinely gathered to gain insights into complex processes such as behavioral, biological, or physical processes. Challengingly, such data no…
On the satisfaction frequency of spectral characterization conditions
Nikita Lvov, Alexander Van Werde
We give the first specific conjectures on how frequently graphs satisfy sufficient conditions for being uniquely characterized by spectral information. These conjectures arise from…
Are sparse graphs typically determined by their spectrum?
Nils Van de Berg, Alexander Van Werde
We investigate whether it is typical for a sparse graph to be uniquely characterized by its adjacency spectrum up to isomorphism. Our first result shows that the giant component of…
A sufficient condition for generalized spectral characterization of graphs with loops
Alexander Van Werde
Sufficient conditions for a simple graph to be characterized up to isomorphism given its spectrum and the spectrum of its complement graph are known due to Wang and Xu. This note e…