%0 Journal Article %1 rapoport1957contribution %A Rapoport, Anatol %D 1957 %I Springer New York %J Bulletin of Mathematical Biology %K analysis degree distribution network sna %P 257-277 %R 10.1007/BF02478417 %T Contribution to the theory of random and biased nets %U http://dx.doi.org/10.1007/BF02478417 %V 19 %X 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.

@article{rapoport1957contribution, abstract = {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.}, added-at = {2011-12-08T11:10:59.000+0100}, affiliation = {University of Michigan Mental Health Research Institute USA USA}, author = {Rapoport, Anatol}, biburl = {https://www.bibsonomy.org/bibtex/24fd1893c98176e0c7ec855b72f813c30/folke}, description = {SpringerLink - Bulletin of Mathematical Biology, Volume 19, Number 4}, doi = {10.1007/BF02478417}, interhash = {30c120a093eaf959ec6ac88e998795be}, intrahash = {4fd1893c98176e0c7ec855b72f813c30}, issn = {0092-8240}, issue = {4}, journal = {Bulletin of Mathematical Biology}, keyword = {Mathematics and Statistics}, keywords = {analysis degree distribution network sna}, pages = {257-277}, publisher = {Springer New York}, timestamp = {2011-12-08T11:10:59.000+0100}, title = {Contribution to the theory of random and biased nets}, url = {http://dx.doi.org/10.1007/BF02478417}, volume = 19, year = 1957 }