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Portraits of Complex Networks

Abstract

We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows for rigorous statistical comparison between networks. Dynamic processes such as percolation can be visualized using animation.

About the code

B_matrix.py and B_matrix.cpp take an edgelist file and write the corresponding B-matrix to a file

An edgelist is an M x 2 matrix for a graph with M edges. The C++ code requires nodes be sequential integers numbered from zero, while the python code is slower, but much more flexible (can handle directed networks for example, which the C++ cannot) and forgiving. Python code requires networkx and (optionally) pylab to plot.

Unless the networks are very large, I greatly encourage using the python code instead of the C++. Additionally, networkx has undergone a great deal of updates and the B_matrices.py file might be slightly out of date, requiring small changes to work again. Fair warning, buyer beware, etc.

Various matlab m-files are included for loading a B-matrix from file, trimming empty columns, and computing the distance between two matrices. The latter is accomplished using B_Distance.m, which takes two matrices as input and returns the distance as described in the paper. It will optionally also plot the row-wise distances.

The m-files may also work in octave, an open source "clone" of matlab but I haven't tried so I make no guarantees.

  • Jim Bagrow, 2008-04-17
  • bagrowjp [at] gmail [dot] com

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