Overview

Welcome to the documentation of pathcensus package. It is a Python (3.8+) implementation of structural similarity and complementarity coefficients for undirected (un)weighted networks based on efficient counting of 2- and 3-paths (triples and quadruples) and 3- and 4-cycles (triangles and quadrangles).

Structural coefficients are graph-theoretic measures of the extent to which relations at different levels (of edges, nodes or entire networks) are driven by similarity or complementarity between different nodes. Even though they are defined in purely combinatorial manner they are motivated by geometric arguments which link them to the family of latent space/random geometric graph models. In particular, the geometric view allow the identification of network motifs charactersitic for similarity (triangles) and complementarity (quadrangles). They can be seen as a generalization of the well-known local and global clustering coefficients which summarize the structure of a network in terms of density of ego subgraph(s).

Even though it is a Python package pathcensus is performant as its main workhorse functions are just-in-time (JIT) compiled to efficient C code thanks to the numba library. It is compatible with numpy arrays and scipy sparse matrices making it easy to use in practice. Moreover, it allows registering graph classes implemented by different third-party packages such as networkx so they can be converted automatically to sparse matrices. Conversion methods for networkx, igraph and graph-tool are registered automatically provided the packages are installed.

Note

pathcensus is compatible only with Python versions supported by numba. In practice it means that it is compatible with all versions (starting from 3.8) except for the latest one, which usually starts to be supported by numba with some (often significant) delay.

For the sake of convenience pathcensus provides also implementations of most appropriate null models for statistical calibration of structural coefficients which are simple wrappers around the excellent NEMtropy package [VBM+21]. It also defines the pathcensus.inference submodule with utility class for facilitating approximate statistical inference based on sampling from null models.

How to cite?

You find the package useful? Please cite our work properly.

Main theory paper

Talaga, S., & Nowak, A. (2022). Structural measures of similarity and complementarity in complex networks. Scientific Reports, 12(1), 16580. https://doi.org/10.1038/s41598-022-20710-w

Contents

• Installation
• Path census & structural coefficients
• Null models
• Approximate statistical inference
• Integration with graph-like classes
• References
• About
• Contributing
• pathcensus

Feedback

If you have any suggestions or questions about Path census feel free to email me at stalaga@protonmail.com.

If you encounter any errors or problems with Path census, please let me know! Open an Issue at the GitHub http://github.com/sztal/pathcensus main repository.