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Graph signal

As explained in Graph Neural Networks in Action

A graph signal is data consisting of values or features defined on the nodes of a graph, typically represented as a vector over those nodes.

A graph signal is a vector of values defined over a graph’s nodes. Each node receives a signal value or feature, allowing node-level data to be processed together with graph structure. section 3.4.3

Graph signals provide the data that graph convolution operates on. Unlike image pixels arranged on a fixed grid, graph nodes have relational, non-Euclidean structure and no predefined ordering. section 3.4.1

A graph-signal workflow connects node data to graph operators:

  • Represent node values as vector x, the graph signal. section 3.4.3
  • Combine x with structural matrices such as the adjacency matrix A and Laplacian matrix L. section 3.4.3
  • Use spatial or spectral methods to identify patterns across connected nodes. section 3.4.1
  • Feed the resulting information into GCN aggregation, where normalized neighbor contributions address large degree differences. section 3.4.3

Visualizing a graph signal

Imagine a graph whose vertices each have a vertical bar. The bar’s height represents the signal value at its originating node; a random positive signal therefore appears as different bar heights across the graph.

How Graph Neural Networks in Action covers it

How deep it goes
Defines the signal as vector x, then places it among adjacency, Laplacian, eigenvector, and Fourier-transform operations.
Examples
Illustrates node values as vertical bars and contrasts graph signals with image pixels on a fixed grid.
What you can do after
Evaluate/understand how node-valued data enters spatial, spectral, and GCN convolution operations.
How it connects
Connects graph convolution, spectral convolution, adjacency matrices, Laplacian matrices, and GCN aggregation.
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Related concepts

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.