Spitz - Optimal edge weight reduction with targeted spectral radius

This code implements the Spitz method as published in XXXXX [link]

Check example.m for an example usage

The methods expects three variables:

• Tthe adjacency matrix A
• The spectral radius beta
• An option structure options (optional)

First import two folders

addpath('projections/'); 
addpath('lbfgs/');

The edges problem:

To solve the problem using the dykstra method:

X_dykstra = near_bounded_sparse(A, beta, options);

To solve the problem using the interior points method:

X_intp = near_bounded_interior_p(A, beta, options);

To solve the problem using the dynamical importance method:

X_dynamical_importance = binary_deletion_dynamical_importance(A, beta, options);

To get the discrete soultion from continuous solution:

W_binary = remove_edges_binarysearch( A, X_dykstra_v ,beta);

The vertices problem:

For the vertices problem you also need to create a "vertices influence matrix":

P = createVerticesInfluenceMatrix(A, 'equal_weight');

To solve the problem using the dykstra method:

X_dykstra_v = near_bounded_sparse_vertices(A, beta, P, options);

To solve the problem using the interior points method:

X_intp_v = near_bounded_interior_p_vertices(A, beta, P, options);

To solve the problem using the dynamical importance method:

X_dynamical_importance_v = binary_deletion_dynamical_importance_vertices(A, beta, options);

To get the discrete soultion from continuous solution:

W_binary = remove_vertices_logsearch( A, X_dykstra_v ,beta);

To reproduce the experiment you can download the networks from koblenz network data: Go to the data folder and run the script download_networks.m. It will create a subfolder under data called net_mat with the networks.

The projections folder contains projection function that are used by the methods.

The data folder contains data for the real world networks.

The lbfgs folder contains functions to run lbfgs with box constraints provided by Stephen Becker and Peter Carbonetto http://www.mathworks.com/matlabcentral/fileexchange/35104-lbfgsb--l-bfgs-b--mex-wrapper

The Dynamical importance method was implemented from the paper by Restrepo et al. http://arxiv.org/abs/cond-mat/0606122

Second order Dynamical importance by Milanese et al. http://journals.aps.org/pre/abstract/10.1103/PhysRevE.81.046112