User pavlo dzikovsky - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T02:33:18Z http://mathoverflow.net/feeds/user/9538 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/39946/transitive-closure-of-multigraphs/40094#40094 Answer by Pavlo Dzikovsky for Transitive closure of multigraphs Pavlo Dzikovsky 2010-09-27T06:06:00Z 2010-09-27T06:06:00Z <p>If consider a multigraph as set of nodes and set of relations, where each number of edges between two nodes have correlated relation (i.e. $(a,b) \in R_N$ means that <strong>"a and b are connected by N edges"</strong>), we can make transitive closure for each relation and, therefore, for "entire multigraph". </p> <p>If, by definition, $(a,b) \in R_N \Rightarrow (a,b) \in R_{N-1}$ (i.e. $(a,b) \in R_N$ means that <strong>a and b are connected by N or more edges</strong>), then transitive closure of the induced graph should be same as induced graph of the transitive closure. </p> <p>Sorry for my english :-(</p>