Hi, I'm testing the Katz centrality function in order to use in a project. In order to calculate the Katz centrality and following the graph_tool documentation I supposed that you use: (I - \alpha A) x = \beta x = \beta / (I - \alpha A) = (I + \alpha A + \alpha^2 A^2 + ... ) \beta where I is the identity matrix and there was appllied the geometric series expansion. My first test was to take a simple circular directed graph with 4 nodes. I used the attached test program with the attached graph file. The adjacency matrix for this graph, A, is: 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 I used distinct values of the max_iter parameter and I set \alpha=1. I use 4 unitary vectors as beta parameter in order to obtain the contents of the calculation matrix (I + \alpha A + \alpha^2 A^2 + ... ), I'll call the F matrix. The test results are for \alpha=1: a) max_iter=1, F matrix is: 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 expected matrix, F = I b) max_iter=2, F matrix is: 0.7 0.0 0.5 0.5 0.5 0.7 0.0 0.5 0.5 0.5 0.7 0.0 0.0 0.5 0.5 0.7 when the expected matrix, F = I + A, is: 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 c) max_iter=3, F matrix is: 0.7 0.0 0.5 0.5 0.5 0.7 0.0 0.5 0.5 0.5 0.7 0.0 0.0 0.5 0.5 0.7 the same as for case max_iter=2 when the expected matrix, F = I + A + A^2, is: 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 d) max_iter=4, F matrix is: 0.52 0.30 0.63 0.48 0.48 0.52 0.30 0.63 0.63 0.48 0.52 0.30 0.30 0.63 0.48 0.52 when the expected matrix, F = I + A + A^2 + A^3, is: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 The first finding was that a normalization is done during the intermediate steps of the calculation because the diagonal elements are changing of value. I look at the graph_katz.hh file and i havesome questions: a) Line 72: c_temp[v] += alpha * get(w, *e) * c[s]; when w is not specified, What w value is used? The normalized adjacency matrix value? b) Line 87: c_temp[v] /= norm; after the swap of the line 90. Could be this the intermediate step nomralization? Is this correct? Thanks in advance, David. katz.py <http://main-discussion-list-for-the-graph-tool-project.982480.n3.nabble.com/file/n4025165/katz.py> test4.xml <http://main-discussion-list-for-the-graph-tool-project.982480.n3.nabble.com/file/n4025165/test4.xml> -- View this message in context: http://main-discussion-list-for-the-graph-tool-project.982480.n3.nabble.com/... Sent from the Main discussion list for the graph-tool project mailing list archive at Nabble.com.