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GRAPH-CENTRALITY

betweenness_centrality

Compute the shortest-path betweenness centrality for nodes.

Example of usage

Compare route hubs using betweenness_centrality on a connected transport network.

Usage / limitations

+Use when: Analyse structural relationships, hub importance or likely missing connections in a transport network.

−Limitations: Depends on network structure, directedness, graph connectivity and the assumptions of the selected measure.

Mathematical formula

Network measure computed over the hub graph; consult the method definition for its mathematical expression.
Sample dataShow 
{
  "variable": "transport_network",
  "domain": "Regional transport network connectivity",
  "nodes": [
    [
      "Hub-A",
      {
        "community": 0,
        "route_group": 0,
        "passengers": 1
      }
    ],
    [
      "Hub-B",
      {
        "community": 0,
        "route_group": 0,
        "passengers": 2
      }
    ],
    [
      "Hub-C",
      {
        "community": 0,
        "route_group": 0,
        "passengers": 3
      }
    ],
    [
      "Hub-D",
      {
        "community": 1,
        "route_group": 1,
        "passengers": 4
      }
    ],
    [
      "Hub-E",
      {
        "community": 1,
        "route_group": 1,
        "passengers": 5
      }
    ],
    [
      "Hub-F",
      {
        "community": 1,
        "route_group": 1,
        "passengers": 6
      }
    ]
  ],
  "edges": [
    [
      "Hub-A",
      "Hub-B"
    ],
    [
      "Hub-A",
      "Hub-C"
    ],
    [
      "Hub-B",
      "Hub-C"
    ],
    [
      "Hub-C",
      "Hub-D"
    ],
    [
      "Hub-D",
      "Hub-E"
    ],
    [
      "Hub-D",
      "Hub-F"
    ],
    [
      "Hub-E",
      "Hub-F"
    ]
  ],
  "directed_edges": [
    [
      "Hub-A",
      "Hub-B"
    ],
    [
      "Hub-B",
      "Hub-C"
    ],
    [
      "Hub-C",
      "Hub-D"
    ],
    [
      "Hub-D",
      "Hub-E"
    ],
    [
      "Hub-E",
      "Hub-F"
    ],
    [
      "Hub-F",
      "Hub-A"
    ],
    [
      "Hub-A",
      "Hub-C"
    ],
    [
      "Hub-C",
      "Hub-E"
    ]
  ]
}

Code example (Python)

# DataLens.ai example — transport network analytics.
# The named transport_network sample is included when copying input + code + test.
import math
import networkx as nx

# Construct an undirected network of connected transport hubs.
G = nx.Graph()
G.add_nodes_from((name, attrs) for name, attrs in transport_network["nodes"])
G.add_edges_from(transport_network["edges"])
# Construct a directed route network when direction is relevant.
D = nx.DiGraph()
D.add_nodes_from((name, attrs) for name, attrs in transport_network["nodes"])
D.add_edges_from(transport_network["directed_edges"])

# Evaluate betweenness_centrality using the network's named hubs.
result = nx.betweenness_centrality(G)
# Verify the result contains meaningful values for this network.
assert result is not None
assert isinstance(result, (dict, list, float, int))
assert len(result) > 0 if isinstance(result, (dict, list)) else math.isfinite(float(result))
# Successful execution and assertions confirm the example.
print("Expected output verified")