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## Re: [igraph] Bridges between clusters

 From: Stephan Schlögl Subject: Re: [igraph] Bridges between clusters Date: Wed, 25 Jun 2014 18:00:07 +0200 User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:24.0) Gecko/20100101 Thunderbird/24.5.0

 Hi, thanks for the link I'm going to have a look at it soon. Here is what i came up with based on the instructions you sent me. The function takes g    igraph object att    the name of the vertex attribute containing the community membership mode    the neigbhorhood mode c("in","out","all"), which is directly passed to igraphs neighboorhood function calc    the type of calculation to be done c("membscore","expent"), where membscore (for membership score) is supposed to be the first option you suggested and expent (for expontiated entropy of the memebership score vector) which hopefully implements your second suggestion it returns a vector of the length length(V(g)) with the respective bridgeness score for each vertex. bridgeness <- function(g,att,mode="all",calc="membscore"){     require(igraph)         membscore <- function(input){             nbc <- get.vertex.attribute(g, att, index=V(g)[input])             result <- subset(count(nbc[1]==nbc[2:length(nbc)]),x==TRUE)\$freq/(length(nbc)-1)             return(-(result-1))         }         expent <- function(input){             nbc <- get.vertex.attribute(g, att, index=V(g)[input])             if(length(nbc)>1){                 membv <- count(nbc[2:length(nbc)])\$freq/(length(nbc)-1)                 result <- exp(-(sum(log(membv)*membv)))}                 else{result <- 0}             return(result)         }     nbs <- neighborhood(g,1,mode=mode)     result <- unlist(lapply(nbs,calc))     return(result) } It would be great if you find the time to have a look at it and tell me if it does what you recommended me to do. Thanks a lot for your help! Best, stephan On 24.06.2014 15:14, Tamás Nepusz wrote: How about using this paper by our own Dr Nepusz? http://arxiv.org/abs/0707.1646 That's nice Actually, the clustering algorithm described in that paper probably won't scale up to the size of the graph you are working with. However, you can probably still make use of the "bridgeness" measure by "making up" membership scores for each vertex and each cluster as follows. Let vertex i belong to cluster j with a score that corresponds to the total weight of edges connecting vertex i to members of cluster j, divided by the total weight of edges incident on vertex i. You can then either calculate "bridgeness" scores from these membership scores. Alternatively, you can calculate the exponentiated entropy of the membership score vector corresponding to a single vertex -- this gives you the "effective number of clusters" that the vertex belongs to. For instance, if 60% of the edges of a vertex connect the vertex to cluster 1, 30% of the edges connect it to cluster 2 and 10% connect it to cluster 3, the membership vector is defined as [0.6, 0.3, 0.1]. The exponentiated entropy of this vector is then exp(-(0.6*log(0.6) + 0.3*log(0.3) + 0.1*log(0.1))), which tells us that the vertex effectively belongs to 2.45 clusters. If the membership vector were [0.9, 0, 0.1], the exponentiated entropy would have yielded exp(-0.9*log(0.9)-0.1*log(0.1)) 1.38. You can then set an arbitrary threshold and say that the bridges are those vertices for which the exponentiated entropy is above 1.5. T. _______________________________________________ igraph-help mailing list address@hidden https://lists.nongnu.org/mailman/listinfo/igraph-help On 25.06.2014 12:10, Tamás Nepusz wrote: thank you very much for your fast answers. Based on the abstract of  Tamas paper this is exactly what i was looking for. Hopefully I can use  this for smaller networks in the future. Is it implemented in igraph for R? It is implemented using igraph, but it does not use R - it uses the C core directly. The source code is available here: https://github.com/ntamas/fuzzyclust I haven't used it in a while so if it doesn't work with the current version of igraph, let me know and I'll try to fix it. Best, T.