Multilayer network tensor factorization, for community detection, link prediction and measure layer interdependence.
Implements the algorithm described in:
De Bacco, C., Power, E. A., Larremore, D. B., & Moore, C. (2017). Community detection, link prediction, and layer interdependence in multilayer networks. Physical Review E, 95(4), 042317.
Copyright (c) 2016 Caterina De Bacco.
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cpp: c++ version of the algorithm. Faster than the Python one.
python: Python version. Slower than c++.
data: Contains sample adjacency files to test the code.
Need to make a directory called
data outside the
To make one, just type from the command line, inside that folder:
The multilayer adjacency matrix should be formatted as an edge list with L+3 columns:
E node1 node2 3 0 0 1
The first columns tells the algorithm that the row denotes an edge; the second and third are the source and target nodes of that edge, respectively; l+3 column tells if there is that edge in the l-th layer and the weigth (must be integer). In this example the edge node1 --> node2 exists in layer 1 with weight 3 and in layer 4 with weight 1, but not in layer 2 and 3.
Note: if the network is undirected, you only need to input each edge once. You then need to specificy to the algotihm that you are considering the undirected case: for the
cpp version this is done by running
./MultiTensor_undirected (first you need to compile it by changing the Makefile accordingly); for the
python version this is done by giving as a command line input parameter
Three files will be generated inside the
data folder: the two NxK membership matrices
V, and the KxK layer affinity matrix
W. Supposing that K=4 and
E=".dat" the output files will be inside
data folder with names:
The first line outputs the Max Likelihood among the realizations. For the membership files, the subsequent lines contain L+1 columns: the first one is the node label, the follwing ones are the (not normalized) membership vectors' entries. For the affinity matrix file, the subsequent lines start with the number of the layer and then the matrix for that layer. For the restricted assortative version only the diagonal entries of the affinity matrix are printed. The first entry of each row is the layer index.