Created in 2021

Author: Flaviano Morone

**** BANDWIDTH CLUSTERING **** Figure1(a)

To compile the source code download the files "opp.h" and "opp_bandwidth.c" and put them in the same folder.

Open a terminal and type: gcc -o opp opp_bandwidth.c -lm -O3

To run the executable file type: ./opp graph.txt p

• graph.txt - is the input file containing the graph formatted as an adjacency matrix. Start with a graph with N < 100 nodes (you should be able to run the algorithm on graphs up to N ~ O(10^3) nodes).

• p - is a float between 0 and 1, measuring the bandwidth of the clustering. Start with p = 0.5.

The program outputs four files: bandwidth_r0.50_graph.txt, bandwidth_s0.50_graph.txt, bandwidth_x0.50_graph.txt, bandwidth_b0.50_graph.txt

To plot the energy (cost) function open gnuplot and type: plot 'bandwidth_r0.50_graph.txt' u 2:3 w dots

To plot the error function open gnuplot and type: plot 'bandwidth_r0.50_graph.txt' u 2:4 w dots

To plot the clustered graph open gnuplot and type: set view map, splot 'bandwidth_s0.50_graph.txt' u 1:2:3 w p pt 5 palette

To plot the optimal permutation matrix open gnuplot and type: set view map, splot 'bandwidth_x0.50_graph.txt' u 1:2:3 w p pt 5 palette

To plot the input graph open gnuplot and type: set view map, splot 'bandwidth_b0.50_graph.txt' u 1:2:3 w p pt 5 palette

**** NESTEDNESS CLUSTERING **** Figure1(b)

To compile the source code download the files "opp.h" and "opp_nestedness.c" and put them in the same folder.

Open a terminal and type: gcc -o opp opp_nestedness.c -lm -O3

To run the executable file type: ./opp graph.txt p

• graph.txt - is the input file containing the graph formatted as an adjacency matrix. Start with a graph with N < 100 nodes (you should be able to run the algorithm on graphs up to N ~ O(10^3) nodes).

• p - is a float between 0 and 1, measuring the curvature of the nested region of the matrix. The smaller the - p - the higher is the nestedness. Start with p = 0.5.

The program outputs four files: nestedness_r0.50_graph.txt, nestedness_s0.50_graph.txt, nestedness_x0.50_graph.txt, nestedness_b0.50_graph.txt

To plot the energy (cost) function open gnuplot and type: plot 'nestedness_r0.50_graph.txt' u 2:3 w dots

To plot the error function open gnuplot and type: plot 'nestedness_r0.50_graph.txt' u 2:4 w dots

To plot the clustered graph open gnuplot and type: set view map, splot 'nestedness_s0.50_graph.txt' u 1:2:3 w p pt 5 palette

To plot the optimal permutation matrix open gnuplot and type: set view map, splot 'nestedness_x0.50_graph.txt' u 1:2:3 w p pt 5 palette

To plot the input graph open gnuplot and type: set view map, splot 'nestedness_b0.50_graph.txt' u 1:2:3 w p pt 5 palette

**** BOXED CLUSTERING **** Figure1(c)

To compile the source code download the files "opp.h" and "opp_square.c" and put them in the same folder.

Open a terminal and type: gcc -o opp opp_square.c -lm -O3

To run the executable file type: ./opp graph.txt Q

• graph.txt - is the input file containing the graph formatted as an adjacency matrix. Start with a graph with N < 100 nodes (you should be able to run the algorithm on graphs up to N ~ O(10^3) nodes).

• Q - is an integer Q = 2,3,4,... counting the number of boxes the matrix will be clustered into. Start with Q = 5.

The program outputs four files: square_r5_graph.txt, square_s5_graph.txt, square_x5_graph.txt, square_b5_graph.txt

To plot the energy (cost) function open gnuplot and type: plot 'square_r5_graph.txt' u 2:3 w dots

To plot the error function open gnuplot and type: plot 'square_r5_graph.txt' u 2:4 w dots

To plot the clustered graph open gnuplot and type: set view map, splot 'square_s5_graph.txt' u 1:2:3 w p pt 5 palette

To plot the optimal permutation matrix open gnuplot and type: set view map, splot 'square_x5_graph.txt' u 1:2:3 w p pt 5 palette

To plot the input graph open gnuplot and type: set view map, splot 'square_b5_graph.txt' u 1:2:3 w p pt 5 palette

**** TRIANGULAR CLUSTERING **** Figure1(d)

To compile the source code download the files "opp.h" and "opp_triangular.c" and put them in the same folder.

Open a terminal and type: gcc -o opp opp_triangular.c -lm -O3

To run the executable file type: ./opp graph.txt Q

• graph.txt - is the input file containing the graph formatted as an adjacency matrix. Start with a graph with N < 100 nodes (you should be able to run the algorithm on graphs up to N ~ O(10^3) nodes).

• Q - is an integer Q = 2,3,4,... counting the number of triangles the matrix will be clustered into. Start with Q = 3.

The program outputs four files: triangular_r3_graph.txt, triangular_s3_graph.txt, triangular_x3_graph.txt, triangular_b3_graph.txt

To plot the energy (cost) function open gnuplot and type: plot 'triangular_r3_graph.txt' u 2:3 w dots

To plot the error function open gnuplot and type: plot 'triangular_r3_graph.txt' u 2:4 w dots

To plot the clustered graph open gnuplot and type: set view map, splot 'triangular_s3_graph.txt' u 1:2:3 w p pt 5 palette

To plot the optimal permutation matrix open gnuplot and type: set view map, splot 'triangular_x3_graph.txt' u 1:2:3 w p pt 5 palette

To plot the input graph open gnuplot and type: set view map, splot 'triangular_b3_graph.txt' u 1:2:3 w p pt 5 palette

**** DIPOLE CLUSTERING **** Figure1(e)

To compile the source code download the files "opp.h" and "opp_dipole.c" and put them in the same folder.

Open a terminal and type: gcc -o opp opp_dipole.c -lm -O3

To run the executable file type: ./opp graph.txt p

• graph.txt - is the input file containing the graph formatted as an adjacency matrix. Start with a graph with N < 100 nodes (you should be able to run the algorithm on graphs up to N ~ O(10^3) nodes).

• p - is a float between 0 and 1, measuring the transversal width of the dipole. Start with p = 0.5.

The program outputs four files: dipole_r0.50_graph.txt, dipole_s0.50_graph.txt, dipole_x0.50_graph.txt, dipole_b0.50_graph.txt

To plot the energy (cost) function open gnuplot and type: plot 'dipole_r0.50_graph.txt' u 2:3 w dots

To plot the error function open gnuplot and type: plot 'dipole_r0.50_graph.txt' u 2:4 w dots

To plot the clustered graph open gnuplot and type: set view map, splot 'dipole_s0.50_graph.txt' u 1:2:3 w p pt 5 palette

To plot the optimal permutation matrix open gnuplot and type: set view map, splot 'dipole_x0.50_graph.txt' u 1:2:3 w p pt 5 palette

To plot the input graph open gnuplot and type: set view map, splot 'dipole_b0.50_graph.txt' u 1:2:3 w p pt 5 palette

**** TRIPOLE CLUSTERING **** Figure1(f)

To compile the source code download the files "opp.h" and "opp_tripole.c" and put them in the same folder.

Open a terminal and type: gcc -o opp opp_tripole.c -lm -O3

To run the executable file type: ./opp graph.txt p

• graph.txt - is the input file containing the graph formatted as an adjacency matrix. Start with a graph with N < 100 nodes (you should be able to run the algorithm on graphs up to N ~ O(10^3) nodes).

• p - is a float between 0 and 1, measuring the transversal width of the tripole. Start with p = 0.5.

The program outputs four files: tripole_r0.50_graph.txt, tripole_s0.50_graph.txt, tripole_x0.50_graph.txt, tripole_b0.50_graph.txt

To plot the energy (cost) function open gnuplot and type: plot 'tripole_r0.50_graph.txt' u 2:3 w dots

To plot the error function open gnuplot and type: plot 'tripole_r0.50_graph.txt' u 2:4 w dots

To plot the clustered graph open gnuplot and type: set view map, splot 'tripole_s0.50_graph.txt' u 1:2:3 w p pt 5 palette

To plot the optimal permutation matrix open gnuplot and type: set view map, splot 'tripole_x0.50_graph.txt' u 1:2:3 w p pt 5 palette

To plot the input graph open gnuplot and type: set view map, splot 'tripole_b0.50_graph.txt' u 1:2:3 w p pt 5 palette

**** QUADRUPOLE CLUSTERING **** Figure1(g)

To compile the source code download the files "opp.h" and "opp_quadrupole.c" and put them in the same folder.

Open a terminal and type: gcc -o opp opp_quadrupole.c -lm -O3

To run the executable file type: ./opp graph.txt p

• graph.txt - is the input file containing the graph formatted as an adjacency matrix. Start with a graph with N < 100 nodes (you should be able to run the algorithm on graphs up to N ~ O(10^3) nodes).

• p - is a float between 0 and 1, measuring the transversal width of the quadrupole components. Start with p = 0.5.

The program outputs four files: quadrupole_r0.50_graph.txt, quadrupole_s0.50_graph.txt, quadrupole_x0.50_graph.txt, quadrupole_b0.50_graph.txt

To plot the energy (cost) function open gnuplot and type: plot 'quadrupole_r0.50_graph.txt' u 2:3 w dots

To plot the error function open gnuplot and type: plot 'quadrupole_r0.50_graph.txt' u 2:4 w dots

To plot the clustered graph open gnuplot and type: set view map, splot 'quadrupole_s0.50_graph.txt' u 1:2:3 w p pt 5 palette

To plot the optimal permutation matrix open gnuplot and type: set view map, splot 'quadrupole_x0.50_graph.txt' u 1:2:3 w p pt 5 palette

To plot the input graph open gnuplot and type: set view map, splot 'quadrupole_b0.50_graph.txt' u 1:2:3 w p pt 5 palette

**** PENTAPOLE CLUSTERING **** Figure1(h)

To compile the source code download the files "opp.h" and "opp_pentapole.c" and put them in the same folder.

Open a terminal and type: gcc -o opp opp_pentapole.c -lm -O3

To run the executable file type: ./opp graph.txt p

• graph.txt - is the input file containing the graph formatted as an adjacency matrix. Start with a graph with N < 100 nodes (you should be able to run the algorithm on graphs up to N ~ O(10^3) nodes).

• p - is a float between 0 and 1, measuring the transversal width of the pentapole components. Start with p = 0.5.

The program outputs four files: pentapole_r0.50_graph.txt, pentapole_s0.50_graph.txt, pentapole_x0.50_graph.txt, pentapole_b0.50_graph.txt

To plot the energy (cost) function open gnuplot and type: plot 'pentapole_r0.50_graph.txt' u 2:3 w dots

To plot the error function open gnuplot and type: plot 'pentapole_r0.50_graph.txt' u 2:4 w dots

To plot the clustered graph open gnuplot and type: set view map, splot 'pentapole_s0.50_graph.txt' u 1:2:3 w p pt 5 palette

To plot the optimal permutation matrix open gnuplot and type: set view map, splot 'pentapole_x0.50_graph.txt' u 1:2:3 w p pt 5 palette

To plot the input graph open gnuplot and type: set view map, splot 'pentapole_b0.50_graph.txt' u 1:2:3 w p pt 5 palette

For more information, visit https://theconceptron.com/assets/opp2.pdf