Weighted network motifs as random walk patterns

Find weighted motifs using a random walk approach

This package contains 2 routines to find wieghted motifs of size 2/3/4 using a novel methodology based on a sink node and random walker. The sink node allows to balance a directed network, while the random walker can detect 8 possibile weighted motifs (see figure). Practically, she is placed on a random node and can move along her neighoburs according to the transition probability matrix associated to the netowrk. Repeating several times the placing&moving it is possible to register the frequency of each weighted motif.

The package contains:

• 2 routines
• a text file with simple command lines to test the routines
• a small real network about macaque grooming (http://konect.cc/networks/moreno_rhesus/)

For details about the methodology, its applications to real networks, the significance of the weighted motifs occurrences, the 8 motifs detectable... take a look at the paper:

Picciolo, F., Ruzzenenti, F., Holme, P., & Mastrandrea, R. (2022). Weighted network motifs as random walk patterns. New Journal of Physics.