toymodel module

toymodel.create_LFR_graph()

Create an Lancichinetti Fortunato Radicchi (LFR) benchmark graph.

The graph has 500 nodes with specific degree and community size distributions. Community labels are then assigned to the nodes.

Returns:

A NetworkX graph with community labels assigned to nodes.

Return type:

networkx.Graph

toymodel.create_SBM_graph()

Create a Stochastic Block Model (SBM) graph with 2 equal size communities.

The sizes of the communities are predefined as 250, 250 (as it is in “Community Detection on Networks with Ricci Flow” by by Chien-Chun Ni et al.). A probability matrix defines the edge probabilities within and across the communities. This function also assigns community labels to the nodes in the graph.

Returns:

A NetworkX graph with community labels assigned to nodes.

Return type:

networkx.Graph

toymodel.run_tests()

Run all tests including graph generation, Ricci curvature computation, accuracy checking, and surgery performance.

The function allows the user to choose between generating a Stochastic Block Model (SBM) graph or an LFR benchmark graph. It then computes the Ricci curvature, performs Ricci flow, checks modularity and ARI, and performs edge surgery on the graph.

Returns:

None

Return type:

None

toymodel.test_check_accuracy(G)

Compute Modularity and Adjusted Rand Index (ARI) for different edge weight cutoffs.

This function tests the community detection performance by checking modularity and ARI for different cutoff values applied to the graph.

Parameters:

G (networkx.Graph) – The graph on which the accuracy is tested.

Returns:

Maximum weight, cutoff range, modularity, and ARI values.

Return type:

tuple

toymodel.test_perform_surgery(G)

Perform edge surgery on the graph by removing edges with weight greater than a given threshold.

The user is prompted to input a threshold value, and edges with weights greater than this threshold are removed from the graph.

Parameters:

G (networkx.Graph) – The graph on which the surgery is performed.

toymodel.test_ricci_curvature(G)

Compute Ricci curvature of the given graph using Ollivier-Ricci method.

This function initializes the Ollivier-Ricci curvature calculation on the input graph and computes the Ricci curvature using the Optimal Transport Distance (OTD) method.

Parameters:

G (networkx.Graph) – The graph to compute the Ricci curvature on.

Returns:

The OllivierRicci instance containing computed Ricci curvature.

Return type:

GraphRicciCurvature.OllivierRicci

toymodel.test_ricci_flow(orc, iterations)

Compute Ricci flow of the graph using Ollivier-Ricci method.

This function applies the Ricci flow algorithm to the graph and updates the graph’s curvature.

Parameters:

orc (GraphRicciCurvature.OllivierRicci) – The OllivierRicci instance that has the initial Ricci curvature.

Returns:

The updated graph after applying Ricci flow.

Return type:

networkx.Graph