Structural Analysis Nestedness, Modularity and In-block

This code performs structural analysis in binary unipartite and bipartite networks by means of in-block nestedness as defined by Solé-Ribalta et al, PRE 2018 (https://doi.org/10.1103/PhysRevE.97.062302), as well as global nestedness and modularity.

Inputs:

1. path-folder = directory where the network data files are. The data files with .csv file extension. It can be either in edge list or adjacency matrix format with no headers.
2. bipartite = boolean value to indicate if "filename" is a bipartite (True) or unipartite (False) network.
3. edge_data = boolean value indicating the format of the data file. Three-column/edge list (True) or matrix format (False).

Outputs:

1. A summary file, data_structures_NQI_results.csv, containing as many rows as input files found in path-folder. Its columns report for each network analysed the name of its input file, and the values of , , and .

2. As many files as input files with general naming in-block_partition_<filename>.csv, where <filename> is the extensionless name of the respective input file. Each files are formed by one or two columns, depending whether the network is unipartite or bipartite. A column contains the indices of the block each node is assigned to by optimizing the in-block nestedness, following zero indexing. Therefore, columns' lengths equal the number of nodes present in the corresponding graph or subgraph. As an example for a bipartite network, the i-th value of the column labelled by rows (columns) indicates the block of the i-th node of the subgraph associated to the rows (columns) of the input adjacency matrix. N.B. block indices are generally not contiguous, namely, the number of blocks does not in principle coincide with the largest block index+1.

3. Like above, but the general naming is modularity_partition_<filename>.csv and partitions are calculated by optimising the modularity.

If for example we pass bipartite=True and edge_data=True, all the networks we want to analyze have to fulfill such conditions.

example:

python structural_analysis.py home/User/data/ True False

Nestedness and In-block nestedness

Both metrics are computed considering the condition to compare the paired overlap between pairs of nodes, in contrast with the NODF metrics that considers

Modularity and in-block nestedness optimization

The optimization of modularity and in-block nestedness is performed by employing the Extremal optimization algorithm (https://doi.org/10.1103/PhysRevE.72.027104). The main code for this function was written in c++ and should be compiled as a file with a .so extension for Python 3.x. This file will be imported in Python as a library.

This will be possible for MacOS or Linux.

System Requirements

Compilers

1. Clang/LLVM 3.3 or newer (for Apple Xcode's clang, this is 5.0.0 or newer) or
2. GCC 4.8 or newer

Python 3.x.

pybind11 (via pip or conda)

To compile the c++ files

Compilation on Linux:

g++ -O3 -Wall -shared -std=c++11 -fPIC `python -m pybind11 --includes` EO_functions_bipartite.cpp -o extremal_bi.so

Compilation on MacOS:

g++ -O3 -Wall -shared -std=c++11 -undefined dynamic_lookup `python -m pybind11 --includes` EO_functions_bipartite.cpp -o extremal_bi.so

Citations

MJ Palazzi, J Borge-Holthoefer, CJ Tessone and A Solé-Ribalta. Macro- and mesoscale pattern interdependencies in complex networks. J. R. Soc. Interface, 16, 159, 20190553 (2019). DOI: 10.1098/rsif.2019.0553

MJ Palazzi, A Solé-Ribalta, V Calleja-Solanas, CA Plata, S Meloni, S Suweis and J Borge-Holthoefer. An ecological approach to structural flexibility in online communication systems. Nature Communications, 12, 1941 (2021). DOI: 10.1038/s41467-021-22184-2