Hi, Sorry for the late response. Most likely there is a bug in how PRPACK treats directed graphs; in theory, there should be no difference between the ARPACK and PRPACK implementations (apart from the latter being faster and more stable), both should treat directed=F and as.undirected() the same way. I was briefly looking at the conversion between an igraph graph and PRPACK's internal data structures in the source code, but I could not find anything yet that could explain the difference; feel free to take a look yourself as well:

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https://github.com/igraph/igraph/blob/master/src/prpack/prpack_igraph_graph.cpp I have added an issue to Github but I don't think I will be able to get around to fixing this any time in the near future, so please chime in if you managed to figure out anything in the meanwhile: https://github.com/igraph/igraph/issues/972 T. On Sat, Nov 19, 2016 at 11:59 AM, danopiacek . <dano.pia...@gmail.com> wrote: > Hello to everyone, > > First of all, I would like to thank the authors of these amazing package. > I use it extensively in my master thesis. > I am sorry for duplicate if there already exists same thread. > > I have a huge network with couple of millions of edges and would like to > calculate personalized PageRank. My network is attributed and I would like > to use edge weights to calculate PageRank. I can either consider my network > as directed or undirected, but in both cases my network is multigraph. I > have encountered several 'strange' results when calculating weighted > PageRank. > > Here I will try to present it on simple networks without 'personalization'. > > 1a.) Example with directed symmetric network, with no multiple edges and > no weights. > A = matrix(c(0,1,1,1,0,0,1,0,0),byrow=T,nrow=3) > g = graph.adjacency(A) > > Then I compute PageRank with page_rank function and get the same result > for both "PRPACK" and "ARPACK" algo. I can also compute via matrix inverse > as follows: > D = diag(1/apply(A,1,sum),nrow(A)); Beta = > (1-0.85)*rep(1/nrow(A),nrow(A)) > (pr.in = Beta%*%solve(diag(1,nrow(A))-0.85*D%*%A)) > And as expected I get the same PageRank score. In addition, if I consider > network as undirected I get the same scores, as expected. > > 1b.) The same example with edge weights. > > set.seed(1) > E(g)$weight = round(runif(ecount(g)),1) > And again, using page_rank I get the same scores for both algorithms. Or I > can get the same scores with weight matrix *W* as: > W = matrix(c(0,0.3,0.4,0.6,0,0,0.9,0,0),byrow=T,nrow=3) > D = diag(1/apply(W,1,sum),nrow(W)); Beta = > (1-0.85)*rep(1/nrow(W),nrow(W)) > (pr.in = Beta%*%solve(diag(1,nrow(W))-0.85*D%*%W)) > However, if I consider this network being undirected, I get different > scores, namely: > g_UN = as.undirected(g,'each') # do not collapse > (prUn1 = page_rank(g,algo='PRPACK', directed = F)$vector) > (prUn2 = page_rank(g,algo='ARPACK', directed = F)$vector) > (prUn3 = page_rank(g_UN, algo='PRPACK')$vector) > (prUn4 = page_rank(g_UN, algo='ARPACK')$vector) > Here scores given by 'ARPACK' are different to those given by 'PRPACK'. > Moreover, with 'ARPACK' I get same scores for both *g_UN*(undirected > network) and for *directed=F*. However 'PRPACK' gives different scores. > I can replicate results for 'ARPACK' with weight matrix, where I take > sum/average of edge weights: > W_UN = matrix(c(0,0.9,1.3,0.9,0,0,1.3,0,0),byrow=T,nrow=3) > D = diag(1/apply(W_UN,1,sum),nrow(W_UN)) > (pr.in = Beta%*%solve(diag(1,nrow(W_UN))-0.85*D%*%W_UN)) > > 2a.) Example with directed multigraph. > > A2 = matrix(c(0,2,1,1,0,0,1,1,0),byrow=T,nrow=3) > g2 = graph.adjacency(A2) > Without considering edge weights both algorithms give the same scores, > which can be also found as > D = diag(1/apply(A2,1,sum),nrow(A2)) > (pr.in = Beta%*%solve(diag(1,nrow(A2))-0.85*D%*%A2)) > > 2b.) Same graph as undirected. > Here again both algorithms give the same score for both *directed=F* and > *as.undirected(g2,'each')*, or: > A2_UN = matrix(c(0,3,2,3,0,1,2,1,0),byrow=T,nrow=3) > D = diag(1/apply(A2_UN,1,sum),nrow(A2_UN)) > (pr.in = Beta%*%solve(diag(1,nrow(A2_UN))-0.85*D%*%A2_UN)) > gives the same scores. > > 2c.) Same graph with edge weights-directed. > set.seed(1) > E(g2)$weight = round(runif(ecount(g2)),1) > And again I get different scores > page_rank(g2,algo='PRPACK')$vector > page_rank(g2,algo='ARPACK')$vector > Where 'ARPACK' gives the same scores as with weight matrix *W* where edge > weights for multiple > edges(considering direction) are summed > W2 = matrix(c(0,0.7,0.6,0.9,0,0,0.2,0.9,0),byrow=T,nrow=3) > D = diag(1/apply(W2,1,sum),nrow(W2)) > (pr.in = Beta%*%solve(diag(1,nrow(W2))-0.85*D%*%W2)) > > 2d.) Same graph with edge weights-undirected. > g2_UN = as.undirected(g2,'each') # do not collapse > Again, 'PRPACK' and 'ARPACK' give different scores. Moreover, 'PRPACK' > differs for > (prUn1 = page_rank(g2,algo='PRPACK',directed = F)$vector) > (prUN2 = page_rank(g2_UN,algo='PRPACK')$vector) > , while 'ARPACK' gives same scores for both. Or with weight matrix *W *I > can replicate 'ARPACK' by summing edge weights: > W2_UN = matrix(c(0,1.6,0.8,1.6,0,0.9,0.8,0.9,0),nrow=3,byrow = T) > D = diag(1/apply(W2_UN,1,sum),nrow(W2_UN)) > (pr.in = Beta%*%solve(diag(1,nrow(W2_UN))-0.85*D%*%W2_UN)) > > I have examined .c files (centrality.c, arpack.c) and I know that 'ARPACK' > treats *directed=F* and *as.undirected() *same. > > So the main questions are, how does 'PRPACK' treat these two options and > moreover why 'PRPACK' gives different results than 'ARPACK'/weight matrix. > > Thank you very much. > Daniel Piacek > > > > > _______________________________________________ > igraph-help mailing list > igraph-help@nongnu.org > https://lists.nongnu.org/mailman/listinfo/igraph-help > >

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