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- W203460111 abstract "Consider graphs on the vertex set V={1, 2, …, n}, 1 < n < ∞, in which the edge between vertices i and j occurs with probability pij=pji, O≤pij≤ 1, independently for all edges. Let P=(pij) be the n × n symmetric matrix of edge probabilities with pij=0, i=1, …, n. Let T be the random number of spanning trees. E(TP) denotes the redundancy, i.e., the expected number of spanning trees in random graphs with edge probability matrix P. An explicit (determinantal) formula for the sensitivity of the redundancy to changes in any edge probability, namely, ∂E(TP)/∂pij, shows that this sensitivity equals the redundancy of random graphs in which vertices i and j have been collapsed to a single vertex or are connected with probability 1. There is an analogous formula for directed graphs." @default.
- W203460111 created "2016-06-24" @default.
- W203460111 creator A5010543213 @default.
- W203460111 date "1987-01-01" @default.
- W203460111 modified "2023-09-27" @default.
- W203460111 title "The Sensitivity of Expected Spanning Trees in Anisotropic Random Graphs" @default.
- W203460111 cites W2131204490 @default.
- W203460111 doi "https://doi.org/10.1016/s0304-0208(08)73045-7" @default.
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