Directed Measures

Definition

Directed hypergraphs distinguish source and target node sets for each hyperedge.

You will learn

Compute directed measures and compare in- vs out-structure effects.

Overview

• Compute directed hypergraph measures and interpret in/out effects.

• Compare directed vs undirected behavior on examples.

Setup

import matplotlib as mpl

mpl.rcParams.update({
    "figure.figsize": (6, 4),
    "figure.dpi": 120,
    "savefig.dpi": 150,
})

import hypergraphx as hgx

edges = [
    ((1,), (2,)),         # Edge 1: Simple directed edge from 1 to 2
    ((2,), (1,)),         # Edge 2: Simple directed edge from 2 to 1 (reciprocal with Edge 1)
    ((2, 3), (4,)),       # Edge 2: Directed hyperedge with sources 2, 3 and target 4
    ((4,), (2, 3)),       # Edge 3: Directed hyperedge from 4 to targets 2, 5
    ((5,), (1,)),         # Edge 4: Directed edge from 5 to 1 (reciprocal with Edge 1)
    ((6,), (3, 4)),       # Edge 5: Directed hyperedge from 6 to targets 3 and 4
    ((7,), (2, 6)),       # Edge 6: Directed hyperedge from 7 to targets 2 and 6
    ((3, 8), (5,)),       # Edge 7: Directed hyperedge with sources 3, 8 and target 5
    ((4, 5), (7, 8))      # Edge 8: Directed hyperedge with sources 4, 5 and targets 7, 8
]

h = hgx.DirectedHypergraph(edges)

from hypergraphx.measures.directed import in_degree, out_degree, in_degree_sequence, out_degree_sequence

print("In-degree of node 1:", in_degree(h, 1))
print("In-degree of node 2:", in_degree(h, 2))
print("Out-degree of node 1:", out_degree(h, 1))
print("Out-degree of node 2:", out_degree(h, 2))

In-degree of node 1: 1
In-degree of node 2: 2
Out-degree of node 1: 2
Out-degree of node 2: 3

print("In-degree sequence: ", in_degree_sequence(h))
print("Out-degree sequence: ", out_degree_sequence(h))

In-degree sequence:  {1: 1, 2: 2, 3: 2, 4: 2, 5: 2, 6: 1, 7: 1, 8: 1}
Out-degree sequence:  {1: 2, 2: 3, 3: 2, 4: 2, 5: 1, 6: 1, 7: 1, 8: 1}

from hypergraphx.measures.directed import hyperedge_signature_vector

v = hyperedge_signature_vector(h)
print("Hyperedge signature vector: ", v)

Hyperedge signature vector:  [3. 3. 0. 2. 1. 0. 0. 0. 0.]

from hypergraphx.measures.directed import exact_reciprocity, strong_reciprocity, weak_reciprocity

print("Exact reciprocity: ", exact_reciprocity(h, max_hyperedge_size=4))
print("Strong reciprocity: ", strong_reciprocity(h, max_hyperedge_size=4))
print("Weak reciprocity: ", weak_reciprocity(h, max_hyperedge_size=4))

Exact reciprocity:  {2: 0.6666666666666666, 3: 0.4, 4: 0.0}
Strong reciprocity:  {2: 0.6666666666666666, 3: 0.4, 4: 0.0}
Weak reciprocity:  {2: 0.6666666666666666, 3: 0.6, 4: 1.0}

from hypergraphx.motifs.directed_motifs import *

m = compute_directed_motifs(h, order=3, runs_config_model=0)

Computing observed motifs of order 3...

m['observed']

[((((1,), (2, 3)),), 2),
 ((((1,), (2, 3)), ((2, 3), (1,))), 1),
 ((((1, 2), (3,)),), 1)]