cumulated-net-conn

Overview

The repository cumulated-net-conn contains the Python codes designed to compute cumulated explicit and implicit connectivity probabilities given a generic directed, weighted & temporal network. When using this code, please acknowledge the authors by citing Ser-Giacomi et al. (2021).

Index

This documentation is organized as follows:

• Cumulated connectivity code

  • Description
  • Inputs
  • Outputs

• References

Cumulated connectivity code

Description

• The codes called cumulated_multistep_explicit_connectivity.py and cumulated_multistep_implicit_connectivity.py provide cumulated explicit and implicit connectivity probabilities for every pair of nodes in any temporal, directed weighted network. For the mathematical derivation refer to Ser-Giacomi et al. (2021). The calculation is performed as a sequence of sparse matrix products using the scipy.sparse library.
• The file toy_net_right.dat is the adjacency matrix of the toy network of Figure 5 (panel b) of Ser-Giacomi et al. (2021).

Inputs

The main inputs to run the code are:

• A sequence of adjacency matrices file-names finname describing the snapshots of the temporal network analyzed. The format for any input matrix should be a list omitting null weights (as in toy_net_right.dat). In detail:
  • Each row of the list correspond to a link with non-zero weight.
  • The first element of a row is the origin node, the second is the destination node, the third is the weight of the link between them.
  • For the proper normalization of the weights (that should correspond to probabilities) refer to Ser-Giacomi et al. (2021) and to the toy matrix toy_net_right.dat .
• The number of nodes N in the network.
• The maximum number of steps M considered (the minimum number is by default equal to 1).

Outputs

The output file is a single matrix expressed as a list (omitting null weights) in which each element i,j correspond to the connectivity probability from node i to node j.

References

[Ser-Giacomi et al. 2021] Ser-Giacomi, E., et al. Explicit and implicit network connectivity: Analytical formulation and application to transport processes. Physical Review E 103, 042309 (2021)