Betweenness centrality

As explained in Graph Neural Networks in Action

A graph metric that quantifies how often a node lies on shortest paths between other nodes.

Betweenness centrality measures how often a node lies on shortest paths between source and destination nodes. Nodes appearing on many shortest paths have high centrality and may be influential; nodes appearing rarely have low centrality. section 8.3.4

Use betweenness centrality as engineered node data through this workflow:

• Start with an ETL output such as an edge list. section 8.3.4
• Import the graph into a graph-processing framework and calculate the value for every node. section 8.3.4
• Store values in a dictionary keyed by node ID, then attach them as node features for downstream machine learning. section 8.3.4

Figure 8.15 Steps to preprocess data in PyG. From raw files, there are essentially two paths to prep data for ingestion by a PyG algorithm. The first path, shown here, directly creates an iterator of data instances, which is used by the dataloader. The second path mimics the first but performs this process within the dataloader class.

Place centrality computation within the broader path from raw files to data instances consumed by PyTorch Geometric. section 8.3.4

How Graph Neural Networks in Action covers it

How deep it goes

Explains shortest-path counting and influence interpretation, but stops short of formulas, algorithms, and implementation code.

Examples

Uses edge lists, node-ID dictionaries, and shortest paths between unique node pairs as concrete artifacts and examples.

What it assumes

Assumes graphs with nodes, edges, and source-to-destination paths while explaining the metric’s interpretation from those elements.

What you can do after

Apply it via graph-processing workflows and store computed values as node features for PyTorch Geometric data.

How it connects

Connects graph processing, feature engineering, node features, ETL, and PyTorch Geometric.

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Also explained in

• 

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

  liveBookmanning.com
  Knowledge Graphs and LLMs in ActionBetweenness centrality is a graph metric based on how often a 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.

This explainer was generated by Manning's knowledge graph from the text of Graph Neural Networks in Action. The section links point to the parts of the book it draws on.