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The 36 pages that link to Adjacency matrix, each with the reason it gives.

• Graph theoryRelated: This representation translates graph structure into algebraic form.

• Directed graphRelated: For directed graphs, its entries preserve which endpoint is the source.

• Graph (discrete mathematics)Related: It represents graph connections in a form suited to algebra and computation.

• Incidence matrixCompared with: It records vertex-to-vertex adjacency, unlike an incidence matrix's vertex-to-edge relation.

• Edge (graph theory)Related: Its entries provide a matrix representation of edge connections.

• Social network analysisRelated: It encodes who is connected to whom in a form suitable for computation.

• PageRankRelated: It provides a compact representation of the links from which PageRank's transition probabilities are built.

• MultigraphRelated: Its entries can count the number of edges between each pair of vertices.

• Degree (graph theory)Related: For simple graphs, row sums give vertex degrees.

• Directed acyclic graphRelated: Matrix powers can encode directed walks and help characterize cycle structure.

• Graph isomorphismRelated: A vertex bijection preserves adjacency precisely when it reorders one graph's matrix into the other's.

• Simple graphRelated: For a simple graph, its adjacency matrix is symmetric with a zero diagonal.

• Square matrixBroader topic: A graph with the same vertex set for rows and columns has a square adjacency matrix.

• Weighted graphRelated: Weighted graphs commonly store each edge's value in the corresponding matrix entry.

• Adjacency listCompared with: It offers faster edge-existence checks at the cost of space proportional to the square of the vertex count.

• Dependency graphRelated: It represents direct dependency edges in a form useful for matrix-based analysis.

• Network scienceRelated: It turns a network’s connections into a form suited to computation and analysis.

• Path graphRelated: For a path graph, its matrix has nonzero entries only beside the main diagonal, under path ordering.

• Transitive closureRelated: Its Boolean powers represent paths, providing an algebraic route to closure.

• Undirected graphRelated: For a simple undirected graph, its adjacency matrix is symmetric.

• Graph embeddingRelated: Matrix representations make adjacency-preservation conditions explicit.

• Induced subgraphRelated: Restricting it to selected vertices gives the induced subgraph's adjacency matrix.

• Graph automorphismRelated: A vertex permutation is an automorphism exactly when it leaves this matrix unchanged under relabeling.

• Graph homomorphismRelated: The homomorphism condition can be checked by testing every source edge against target adjacency.

• Regular graphRelated: Its row sums equal vertex degrees, making regularity visible algebraically.

• Degree matrixRelated: Its row sums give vertex degrees for simple undirected graphs.

• Floyd–Warshall algorithmRelated: Its distance matrix starts with direct edge weights and is updated in place.

• Graph isomorphism problemRelated: Permuting its rows and matching columns expresses vertex relabeling.

• Spectral graph theoryRelated: Its eigenvalues encode structural information such as walks, connectivity, and regularity.

• Kirchhoff's theoremRelated: It helps define the Laplacian whose cofactor counts trees.

• Laplacian matrixRelated: Subtracting this matrix from the degree matrix gives the combinatorial Laplacian.

• Erdős–Gallai theorem (degree sequences)Related: A degree sequence can be realized by a symmetric zero-one adjacency matrix with zero diagonal.

• Hosoya indexCompared with: It represents direct adjacency, whereas the Hosoya index summarizes all matchings.

• Directed networkRelated: Its entries encode each directed connection by its ordered source and destination.

• Multilayer and multiplex networksRelated: Each layer can be represented by its own adjacency matrix.

• Network formation & growthRelated: Comparing adjacency matrices across time makes link changes explicit.