GRaphlet-orbit ADjacency COunter (GRADCO)

Introduction

This is our alpha-version of GRADCO, our general purpose counter that can output graphlet degree vectors (GDVs), edge graphlet degree vectors, graphlet adjacency matrices, edge orbit adjacency matrices and node orbit adjacency matrices. GRADCO is part of our submission 'Graphlets correct for the topological information missed by random walks' (DOI:10.48550/arXiv.2405.14194), in which we formally define the topological information that is implicitly captured by random walks in terms of orbit adjacencies (i.e., the co-occurence of nodes on symmetric positions within graphlets). We mathematically prove random walks miss various orbit adjacencies and illustrate that these orbit adjacencies have real-world value in a multiclass label prediction setting. If you use GRADCO, please cite our paper.

Quick start guide

We are working on improving the documentation. For now, we provide the example code below to illustrate how to use our counter, GRADCO.

import gradco as gradco
import networkx as nx
from scipy.sparse import csr_array


def main():

    # generate a random graph
    n = 1000
    m = 10
    G = nx.barabasi_albert_graph(n, m, seed=42)
    A = nx.to_scipy_sparse_array(G)

    # create GRADCO counter object
    counter = gradco.Counter(A)

    # count the orbit adjacency matrices
    counter.count()

    # iterate over the orbit adjacencies
    for hop, o1, o2, A in counter.generate_orbit_adjacencies():
        print("O:", hop, o1, o2)

    # iterate the graphlet adjacencies
    for graphlet, A in enumerate(counter.generate_graphlet_adjacencies()):
        print("GA:", graphlet)

    # get the graphlet degree vectors
    GDV = counter.get_GDVs()

    # get the edge graphlet degree vectors
    eGDV = counter.get_edge_GDVs()

    # get the edge orbit adjacency matrices
    for e, A in enumerate(counter.generate_edge_orbit_adjacencies()):
        print("EA:", e)

Roadmap

We forsee the following steps to take GRADCO from alpha to full release:

• set up a GitHub workflow to automatically compile and test the code
• set up a GitHub workflow to automatically deploy the code to PyPI
• add windows to the precompiled wheels
• add a bug report template
• add docs
• upgrade to numpy 2.0
• sync versioning and pypi versioning

In the future, we plan to add the following features:

• speed up the counter
• reduce the memory footprint
• add larger graphlets

The best way to support our project is to cite our paper.