Hi Tamas,
Thank you for your reply. As per the Barrat et al. formula used in the manual. It shows weights per triangle are divided by 2. Then as per your calculations, I should get an output value of 0.5. Kindly clarify? Secondly, is binary adjacency matrix is used for above calculations? Regards Gaurav On Wed, Apr 15, 2015 at 10:13 PM, Tamas Nepusz <[email protected]> wrote: > Hi, > > igraph is correct, changing the weight of that single edge does not change > the > weighted transitivity of the vertex. According to the formula in the > manual, > the transitivity of vertex B is calculated by taking the sum of weights in > all > the triangles that the vertex participates in, restricted to only those > edges > that are incident on vertex B, and dividing it by the product of the > degree of > the vertex minus 1 and the strength of the vertex (where the strength is > defined as the sum of the weights of the edges incident on it). In the > case of > your graph, vertex B participates in three triangles: > > B-C-A, B-C-D and B-A-D > > Let us now assume that the weight of each edge is w, except edge B--C > where the > weight is x. In this case, the formula boils down to the following: > > - degree of vertex B is 3 > - strength of vertex B is x+2*w > - total weight of triangle BCA is x+2*w, but we need to restrict it to > edges > incident on B, so we only have x+w > - total weight of triangle BCD is x+2*w, but we need to restrict it again > so we > only have x+w > - total weight of triangle BAD is 3*w, but again, for the same reason, we > have > 2*w only > > Therefore, we have x+w+x+w+w+w=2*x+4*w in the numerator and we also have > (3-1)*(x+2*w) = 2*x+4*w in the denominator. No matter what the exact > weights > are, the transitivity will always be 1. > > T. > > > On 04/15, Gaurav Thareja wrote: > > Hi All, > > > > I am currently analyzing networks using igraph package and calculating > > transitivity values. > > > > I am experiencing a problem, that while using code below, when I try to > > find weighted transitivity value by changing weights on the edges still > the > > value of the node remains the same. Is this an expected property of > > transitivity implementation (Output is in bold). > > > > Thank you for your help. > > > > Regards > > > > Gaurav Thareja > > > > gw <- graph.formula(A-B:C:D:E, B-C:D, C-D) > > E(gw)$weight <- 0.05 > > E(gw)$color <- "grey" > > E(gw)[ V(gw)[name == "B"] %--% V(gw)[name == "C" ] ]$weight <- 0.5 > > E(gw)[ V(gw)[name == "B"] %--% V(gw)[name == "C" ] ]$color <- "red" > > plot(gw) > > transitivity(gw, type="weight", vids = "B", isolates = c("zero")) *[1]* > > transitivity(gw, type="weight", vids = "C", isolates = c("zero")) *[1]* > > > > ======================================================== > > > > #Figure 1: Random value of local clustering coefficent vs weighted > > clustering coefficient. > > > > gw <- graph.formula(A-B:C:D:E, B-C:D, C-D) > > E(gw)$weight <- 0.05 > > E(gw)$color <- "grey" > > E(gw)[ V(gw)[name == "B"] %--% V(gw)[name == "C" ] ]$weight <- 1 > > E(gw)[ V(gw)[name == "B"] %--% V(gw)[name == "C" ] ]$color <- "red" > > plot(gw) > > transitivity(gw, type="weight", vids = "B", isolates = c("zero")) *[1]* > > transitivity(gw, type="weight", vids = "C", isolates = c("zero")) *[1]* > > > _______________________________________________ > > igraph-help mailing list > > [email protected] > > https://lists.nongnu.org/mailman/listinfo/igraph-help > > > -- > T. > > _______________________________________________ > igraph-help mailing list > [email protected] > https://lists.nongnu.org/mailman/listinfo/igraph-help > -- Regards Gaurav Thareja
_______________________________________________ igraph-help mailing list [email protected] https://lists.nongnu.org/mailman/listinfo/igraph-help
