How deeply does Machine Learning Algorithms in Depth cover adjacency matrix?

Defines binary entries, dimensions, undirected symmetry, and out-degree use without developing storage or implementation details.

Adjacency matrix

As explained in Machine Learning Algorithms in Depth

An adjacency matrix is a matrix that records which pairs of graph vertices are connected by edges.

An adjacency matrix A represents graph connectivity. For a graph G=(V,E), set Aij=1 when an edge connects nodes i and j, and 0 otherwise. For an undirected graph, A is symmetric: A=AT. section 11.4

Use the matrix to encode relational structure alongside node and edge information:

Represent N nodes with an N×N adjacency matrix; directed edges need not produce a symmetric matrix. section 11.4
Pair A with the node feature matrix X, whose N×F entries describe F features for each node. section 11.4
Keep edge attributes separately in an M×S edge feature matrix E when M edges have S features each. section 11.4
For PageRank, derive each page’s out-degree from adjacency entries and use it to construct link-following probabilities. section 7.1.1

CORA citation network

Treat each document as a node and each citation as a directed edge. The adjacency matrix records citation relationships, while a binary N×F feature matrix records whether dictionary words occur in each document. section 11.4

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Also explained in

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Optimization Algorithms: AI techniques for design, planning, and control problemsAn adjacency matrix is a matrix whose entries indicate whether pairs of graph nodes are connected, and possibly encode connection weights.
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Graph Neural Networks in ActionAn adjacency matrix is a matrix representation of a graph in which entries encode whether or how strongly pairs of nodes are connected.
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Data Without LabelsAn adjacency matrix is a matrix representing which pairs of nodes in a graph are connected and, when applicable, the connection weights.
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D3.js in Action, Third EditionAn adjacency matrix is a square grid in which rows and columns represent nodes and cells indicate the presence and optionally the weight of connections between them.
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Graph Algorithms for Data ScienceAn adjacency matrix is a square matrix whose elements indicate whether pairs of graph nodes are connected.
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Advanced Algorithms and Data StructuresAn adjacency matrix is a matrix representation of a graph in which entries indicate whether pairs of vertices are connected, and may encode edge information.
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Financial AI in PracticeA matrix whose entries represent whether or how pairs of graph vertices are connected.

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Related concepts

adjacency listalternative to · An adjacency list is a graph representation that associates each vertex with a collection of its neighboring vertices or incident edges.
graphimplements · A graph is a mathematical structure consisting of vertices connected by edges that represent relationships or connections.
graph Laplacianused by · A graph Laplacian is a matrix formed from a graph’s degree and adjacency matrices that encodes connectivity and supports spectral analysis.
encoderused by · An encoder is a component that transforms input data into an encoded representation for subsequent processing, reconstruction, comparison, or transmission.

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