Node degree

As explained in Graph Neural Networks in Action

The degree of a node is the number of graph edges incident to it, subject to conventions such as self-loop counting.

Node degree counts the edges incident to a node, or equivalently its adjacent nodes under the graph’s conventions. It provides a quick measure of local connectivity: low-degree nodes are sparsely connected, while high-degree nodes can dominate unnormalized neighborhood aggregation. section 8.3 section 3.4.3

Use degree statistics as a compact graph-exploration and preprocessing workflow:

• Count edges or adjacent nodes for every node from an adjacency matrix, adjacency list, or graph object. section 5.2.1 section 8.3
• Plot a degree histogram to see common connectivity levels, peaks, tails, and unusually prominent nodes. section 5.2.1 section 8.3.3
• Sort degrees into a rank plot to inspect how quickly connectivity falls from the most connected nodes. section 8.3.3
• Account for disconnected components before interpreting degree statistics or selecting a graph subproblem. section 8.3.3

Amazon Electronics and social graphs

The Amazon co-purchaser graph contains 7,650 nodes and more than 143,000 edges, yet remains very sparse. Most nodes have degree below 10, a second peak appears around 30, and only a few nodes have very high degree. A social-graph workflow uses NetworkX’s degree method, then plots sorted degrees and a histogram; roughly three-fourths of nodes have fewer than 20 adjacent nodes. section 5.2.1 section 8.3.3

Figure 8.13 Visualization and statistics of the social graph and its large connected component. Network visualization using NetworkX default settings (top). A rank plot of node degree of the entire graph (bottom left). We see that about three-fourths of nodes have less than 20 adjacent nodes. A histogram of degree (bottom right).

Compare a degree-rank plot with a degree histogram to see both prominent nodes and the overall connectivity distribution. section 8.3.3

How Graph Neural Networks in Action covers it

How deep it goes

Defines degree and develops counting, ranking, histogramming, and normalization implications without deriving the full GCN equations.

Examples

Demonstrates degree distributions with Amazon Electronics and social graphs using sparse tensors, NumPy, NetworkX, rank plots, and histograms.

What it assumes

Assumes basic graph representations and teaches degree alongside adjacency structures, components, masks, ranks, and subgraphs.

What you can do after

Diagnose graph connectivity and degree imbalance with Python, NumPy, PyTorch, and NetworkX statistics and visualizations.

How it connects

Connects node degree to adjacency matrices, adjacency lists, edge lists, connected components, and GCN message passing.

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Also explained in

• 

  liveBookmanning.com
  Knowledge Graphs and LLMs in ActionNode degree is the number of edges incident to a node, optionally separated by incoming and outgoing direction.
• 

  liveBookmanning.com
  Graph Algorithms for Data ScienceNode degree is the number of graph relationships incident to a node, with directed graphs potentially distinguishing incoming and outgoing relationships.
• 

  liveBookmanning.com
  Fabulous Adventures in Data Structures and AlgorithmsGraph degree is the number of edges incident to a given graph node.

Compare how 4 books explain node degree →

Related concepts

• Adamic-Adar indexused by · The Adamic-Adar index is a link-prediction metric that scores node pairs by weighting common neighbors more highly when they have lower degree.
• common neighbor countmeasured by · Common neighbor count is the number of nodes directly connected to both members of a node pair, often used as a link-prediction score.
• degree-weighted path countused by · A degree-weighted path count is a path-based graph metric that weights paths according to the degrees of the entities they traverse.
• PageRankcontrasts with · PageRank is a link-analysis algorithm that estimates the relative importance of nodes in a directed graph from the structure and importance of incoming links.
• undirected graphcontrasts with · An undirected graph is a graph whose edges have no orientation, so each edge connects its endpoints symmetrically.

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.