The Kronecker product of graphs

Vertex Censored Stochastic Kronecker Product Graphs

Stochastic Kronecker Product Graphs are an interesting and useful class of Generative Network Models. They can be fitted using a fast Maximum Likelihood Estimator and reproduce many important statistical properties commonly found in large real-world networks. However, they suffer from an unfortunate drawback: the need to pad the Stochastic Kronecker Product Graph with isolated vertices. To addr...

Quilting Stochastic Kronecker Product Graphs to Generate Multiplicative Attribute Graphs

We describe the first sub-quadratic sampling algorithm for the Multiplicative Attribute Graph Model (MAGM) of Kim and Leskovec (2010). We exploit the close connection between MAGM and the Kronecker Product Graph Model (KPGM) of Leskovec et al. (2010), and show that to sample a graph from a MAGM it suffices to sample small number of KPGM graphs and quilt them together. Under a restricted set of ...

Isomorphic components of Kronecker product of bipartite graphs

Weichsel (Proc. Amer. Math. Soc. 13 (1962), 47-52) proved that the Kronecker product of two connected bipartite graphs consists of two connected components. A condition on the factor graphs is presented which ensures that such components are isomorphic. It is demonstrated that several familiar and easily constructible graphs are amenable to that condition. A partial converse is proved for the a...

On Edge Exchanges in Hamiltonian Decompositions of Kronecker-product Graphs

Let G be a connected graph on n vertices, and let ; ; and be edge-disjoint cycles in G such that (i) ; (resp. ;) are vertex-disjoint and (ii) jj + jj = jj+ jj = n, where jj denotes the length of. We say that ; ; and yield two edge-disjoint hamiltonian cycles by edge exchanges if the four cycles respectively contain edges e; f; g and h such that each of (? feg) S (? ffg) S fg; hg and (? fgg) S (...

Transformation of the Kronecker Product