Betweenness centrality

As explained in Knowledge Graphs and LLMs in Action

Betweenness centrality is a graph metric based on how often a node lies on shortest paths between other nodes.

Betweenness centrality measures how often a node appears on shortest paths between other node pairs. High-scoring nodes act as bridges and may influence information flow. section 10.1.6

Use the metric to:

• Highlight connectors between otherwise weakly connected research communities. section 6.2
• Find potential bottlenecks, vulnerabilities, and nodes worth monitoring in fraud networks. section 10.1.6
• Compare a node’s bridging role with closeness centrality’s measure of reachability. section 10.1.6

Fraud-network analysis

Compute scores with NetworkX, optionally normalize them to 0–1, round results, and identify key bridges by selecting nodes above the average score. Node A is a prominent bridge in the illustrated fraud graph, while several nodes score zero. section 10.1.6

Figure 6.4 The intellectual influence network comprises the relations TALKED_ABOUT, TALKED_WITH, WORKS_WITH, and STUDENT_OF. Node styling is based on their betweenness centrality score.

Explore an intellectual influence network whose node sizes reflect betweenness centrality, making bridge-like researchers visually prominent. section 6.2

How Knowledge Graphs and LLMs in Action covers it

How deep it goes

Defines shortest-path counting, gives the path-ratio formula, and implements normalized NetworkX scores without deriving the algorithm internally.

Examples

Uses researcher influence graphs, cyclotron-related networks, and a fraud graph containing high-, low-, and zero-scoring nodes.

What it assumes

Assumes graph nodes, node pairs, shortest paths, and basic network metrics while contrasting the concept with closeness centrality.

What you can do after

Diagnose/debug with it: compute bridge scores, summarize their distribution, and flag nodes above the network average.

How it connects

Connects graph analytics with closeness centrality, PageRank, eigenvector centrality, node degree, and fraud detection.

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Also explained in

• 

  liveBookmanning.com
  Graph Neural Networks in ActionA graph metric that quantifies how often a node lies on shortest paths between other nodes.
• 

  liveBookmanning.com
  Graph Algorithms for Data ScienceA betweenness centrality algorithm computes how frequently each node lies on shortest paths between other nodes.

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Related concepts

• closeness centralitycontrasts with · Closeness centrality is a graph metric based on the inverse of a node’s shortest-path distances to other reachable nodes.
• shortest pathmeasures · A shortest path is a path between two nodes or locations that minimizes total distance, length, or cost under a specified measure.
• NetworkXused by · NetworkX is an open-source Python library for creating, manipulating, analyzing, and visualizing graphs and networks.
• signalproduces · A signal is an observable value, event, or pattern that conveys information about a condition, state, or phenomenon.
• nodemeasures · A node is a discrete element in a structured system, such as a graph, tree, network, or distributed system, representing an entity, state, component, or computational unit and potentially connected to other elements.
• normalizationconfigured by · Normalization is the process of transforming a value, representation, or data structure to satisfy a specified standard, scale, or structural constraint.

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