We provide code for constructing different networks that describe the state of dense granular media. This code includes functionality for computing the persistence diagrams using Perseus. For each network we created a separate class. The distribution contains this class together with simple example which computes the persistence of the sample network. See the graphical representation of the sample networks.

Installation:
1) Download Perseus.
2) Download the desired network code:
    - interaction network,
    - position network,
    - digital network (under construction).
3) Copy Perseus to the folder obtained by unpacking the network code.
4) Go to the folder obtained by unpacking the network code and compile it by using the included makefile. This produces an executable file Network.
5) Compute the persistence diagrams of the included sample network. To run the code type ./Network SampleNetwork.txt Persistence. It will read the network from the file SampleNetwork.txt and create files Persistence_0.txt and Persistence_1.txt. The first file contains generators for the 0-dimension persistence diagram and second for the 1-dimension persistence diagram.

How to use the executable file Network?
The executable requires two input variables. The first one is a path to the file containing the network. The second parameter SAVE_AS is a path to the file inot which the persistence generators are stored. The code will produce two files SAVE_AS_0.txt and SAVE_AS_1.txt containing the generators of the persistence diagrams of the given dimension.
 
Required format of the input files for different networks:

1) Interaction network
The input file is a text file. The first line is the number of particles (vertices) N  present in the system. Every other line represents an edge and between two particles and looks as follows: particle_1_ID particle_2_ID value (separated by spaces). The first two entries identify the particles connected by the edge. The entries are integers between 0 and N-1. The variable value corresponds to the value assigned to the edge. NOTE that the file has to end with the value for the last edge and not with  an empty line or an invisible character.

2) Position network
The input file is a text file. The first line is the number of particles (vertices) N. Followed by N lines describing the particles. The format of each line is x_position y_position radius value (separated by spaces). The first two parameters correspond to (x,y) coordinates of the center of a given particle. They are followed by the radius and the value assigned to the particle. NOTE that the file has to end with the value for the last edge and not with  an empty line or an invisible character.

3) Digital network
The input file is a gray scale image where the intensity of the pixel corresponds to its value.

Format of the persistence files.
For each dimension there is one persistence file. It  is a text file and each line corresponds to a single generator. The first entry corresponds to the birth and the second to the death of the generator. We use the supper level set filtration and thus the birth coordinate is larger than the death coordinate. If the death coordinate equals -1 then the generator persist until the end.


NOTE that the code does not carry out the averaging of the network described in Quantifying force networks in particulate systems . If this is desired then open the file Example.cpp and change the line  network.Persistence( input_file.c_str(), output_file.c_str() ); to network.NormalizedPersistence( input_file.c_str(), output_file.c_str() );