Directed Graphs

Not all backbone methods support directed graphs. This guide explains which methods work with directed graphs and how their behavior differs.

Supported methods

The following methods support both directed and undirected graphs:

Statistical methods (all 6):

disparity_filter(), noise_corrected_filter(), marginal_likelihood_filter(), ecm_filter(), lans_filter(), multiple_linkage_analysis()

Structural (2 of 10):

global_threshold_filter(), strongest_n_ties()

Hybrid methods:

glab_filter()

Proximity methods (all 12):

All proximity scoring functions work with directed graphs.

Filters (all 4):

threshold_filter(), fraction_filter(), boolean_filter(), consensus_backbone()

Measures (all 7):

All evaluation functions work with directed graphs.

Undirected-only methods

The following methods raise NetworkXNotImplemented when given a directed graph:

• high_salience_skeleton()

• metric_backbone()

• ultrametric_backbone()

• doubly_stochastic_filter()

• h_backbone()

• modularity_backbone()

• planar_maximally_filtered_graph()

• maximum_spanning_tree_backbone()

• sparsify()

• lspar()

• local_degree()

Behavior differences

For statistical methods on directed graphs, the p-value computation uses the out-degree and out-strength of the source node. noise_corrected_filter() uses the source’s out-strength and the target’s in-strength, and multiple_linkage_analysis() fits each node’s out-links only. For proximity methods on directed graphs, neighborhoods are defined using successors.

glab_filter() follows Section 2.3 of Zhang et al. (2014): each link (i, j) gets an out-importance from the shortest paths that leave i through it (null model on the out-degree of i) and an in-importance from the shortest paths that reach j through it (null model on the in-degree of j); glab_pvalue is the smaller of the two. On a symmetric directed graph this equals the undirected p-value.

Example

import networkx as nx
import nx_backbone as nb

# Create a weighted directed graph
G = nx.DiGraph()
G.add_weighted_edges_from([
    (0, 1, 5.0), (0, 2, 3.0), (0, 3, 1.0),
    (1, 0, 2.0), (1, 2, 4.0),
    (2, 3, 6.0),
])

# Statistical methods work on directed graphs
H = nb.disparity_filter(G)
backbone = nb.threshold_filter(H, "disparity_pvalue", 0.05)