Considers partitions of the vertices of a graph into equal subsets, with few pairs of subsets connected by edges. (Equivalently we view the graph as a subgraph of a product in which one factor is sparse.) A random graph construction shows that such a factorization does not always exist.
We compute the expected numbers of short cycles of each length in certain classes of random graphs used for turbocodes, estimate the probability that there are no such short cycles involving a given vertex, and experimentally verify our estimates. The scarcity of short cycles may help explain the empirically observed accuracy of belief-propagation based error-correction algorithms. Note, the TR, conference, and journal versions of this paper have slightly different titles.
We use random sampling to quickly estimate, for each vertex in a graph, the average distance to all other vertices.
We propose a random graph model that (empirically) appears to have a power law degree distribution. Unlike previous models, our model is based on a Markov process rather than incremental growth. We compare our model with others in its ability to predict web graph clustering behavior.
Graph Theory -- Publications -- David Eppstein -- Theory Group -- Inf. & Comp. Sci. -- UC Irvine
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