11,112 research outputs found
Induced subgraphs in sparse random graphs with given degree sequence
For any , we compute the probability that the subgraph of
induced by is a given graph on the vertex set .
The result holds for any and is further extended to
, the probability space of random graphs with a given
degree sequence .Comment: 31 pages, 11 figure
Properties of Random Graphs with Hidden Color
We investigate in some detail a recently suggested general class of ensembles
of sparse undirected random graphs based on a hidden stub-coloring, with or
without the restriction to nondegenerate graphs. The calculability of local and
global structural properties of graphs from the resulting ensembles is
demonstrated. Cluster size statistics are derived with generating function
techniques, yielding a well-defined percolation threshold. Explicit rules are
derived for the enumeration of small subgraphs. Duality and redundancy is
discussed, and subclasses corresponding to commonly studied models are
identified.Comment: 14 pages, LaTeX, no figure
- …