build_LR.m

Matlab file that takes in input the adjacency matrix of an unweighted graph without repeated edges and returns the corresponding source and target matrices, L and R.

pref.m

Matlab file from the CONTEST toolbox (available at: https://strathprints.strath.ac.uk/15066/) that, given n as input, returns an nxn adjacency matrix built using a preferential attachment type of model (see [50, 52] in the paper). 


script_test_realdata.m

Matlab file that loads an adjacency matrix (stored in the mat file ca-HepTh.mat or Erdos02.mat). The Fiedler vector of the corresponding graph is then used to build increasingly large subgraphs of the original network. For each of these subgraphs, the number of nodes, nonzeros, and the density of the matrices P_1, P_2, and P_3 is computed. This script reproduces figures 4 and 5 in the paper. 

script_test_removal.

Matlab files that computes the number of nodes, edges and the density of the matrices P_1, P_2, P_3, and P_4 built via the smallw or the pref CONTEST functions. The code runs 100 iterations of this process and returns averages and standard deviations. This script reproduces figures 2 and 3. 

smallw.m 

Matlab file from the CONTEST toolbox (available at: https://strathprints.strath.ac.uk/15066/) that, given n as input, returns the nxn adjacency matrix of an independent sample from the class of small world networks described by Watts and Strogatz (see [50, 51] in the paper). 

ca-HepTh.mat

Dataset available from https://sparse.tamu.edu/. See the website for full details. 

Erdos02.mat

Dataset available from https://sparse.tamu.edu/. See the website for full details.