Graphs generated using the Lancichinetti-Fortunato-Radicchi (LFR) model are widely used for assessing the performance of network community detection algorithms. This paper investigates an laternative use of LFR graphs: as training data for learning classifiers that discriminate between edges that are ‘within’ a community and ‘between’ network communities. The LFR generator has a parameter that ...

This paper determines all nonsingular unicyclic mixed graphs on at least nine vertices with at most three Laplacian eigenvalues greater than two.

A mixed graph D is a that can be obtained from by orienting some of its edges. Let α primitive n th root unity, then the α−Hermitian adjacency matrix defined to Hα = [hrs] where hrs if rs an arc in D, sr 1 digon and 0 otherwise. In this paper we study cospectrality Hermitian graph.

A mixed extension of a graph G is a graph H obtained from G by replacing each vertex of G by a clique or a coclique, where vertices of H coming from different vertices of G are adjacent if and only if the original vertices are adjacent in G. If G has no more than three vertices, H has all but at most three adjacency eigenvalues equal to 0 or −1. In this paper we consider the converse problem, a...

In this paper, we discuss some properties of relations between a mixed graph and its line graph, which are used to characterize the Laplacian spectrum of a mixed graph. Then we present two sharp upper bounds for the Laplacian spectral radius of a mixed graph in terms of the degrees and the average 2-degrees of vertices and we also determine some extreme graphs which attain these upper bounds. ©...