The bulletin of mathematical biophysics

, Volume 19, Issue 4, pp 257-277

First online:

Contribution to the theory of random and biased nets

  • Anatol RapoportAffiliated withMental Health Research Institute, University of Michigan

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The probabilistic theory of random and biased nets is further developed by the “tracing” method treated previously. A number of biases expected to be operating in nets, particularly in sociograms, is described. Distribution of closed chain lengths is derived for random nets and for nets with a simple “reflexive” bias. The “island model” bias is treated for the case of two islands and a single axon tracing, resulting in a pair of linear difference equations with two indices. The reflexive bias is extended to multiple-axon tracing by an approximate method resulting in a modification of the random net recursion formula. Results previously obtained are compared with empirical findings and attempts are made to account for observed discrepancies.