Adjacency_matrix - Wikiparency

# Adjacency matrix ## Links (Wikipedia order)  `Adjacency_list` · `Adjugate_matrix` · `Algebraic_graph_theory` · `Alternant_matrix` · `Alternating_sign_matrix` · `Anti-diagonal_matrix` · `Arrowhead_matrix` · `Augmented_matrix` · `Band_matrix` · `Base64` · `Bidiagonal_matrix` · `Bipartite_graph` · `Bisymmetric_matrix` · `Block_matrix` · `Boolean_algebra` · `Boolean_data_type` · `Boolean_matrix` · `Brendan_McKay_(mathematician)` · `Bézout_matrix` · `Cabibbo–Kobayashi–Maskawa_matrix` · `Cartan_matrix` · `Cauchy_matrix` · `Cayley_graph` · `Centering_matrix` · `Centrosymmetric_matrix` · `Characteristic_polynomial` · `Charles_E._Leiserson` · `Circulant_matrix` · `Clifford_Stein` · `Commutation_matrix` · `Companion_matrix` · `Complete_graph` · `Complex_Hadamard_matrix` · [[Computer_science]] · `Conference_matrix` · `Confusion_matrix` · `Connectivity_(graph_theory)` · `Convergent_matrix` · `Copositive_matrix` · `Covariance_matrix` · `DFT_matrix` · `DGML` · `DOT_(graph_description_language)` · `Data_structure` · `Defective_matrix` · `Definite_matrix` · `Degree_(graph_theory)` · `Degree_matrix` · `Density_matrix` · `Design_matrix` · `Design_structure_matrix` · `Determinant` · `Diagonal_matrix` · `Diagonalizable_matrix` · `Diagonally_dominant_matrix` · `Directed_acyclic_graph` · `Directed_graph` · `Discrete_Applied_Mathematics` · `Distance_matrix` · `Doubly_stochastic_matrix` · `Duplication_and_elimination_matrices` · `Edge_list` · `Edmonds_matrix` · `Eigenvalues_and_eigenvectors` · `Elementary_matrix` · `Eric_W._Weisstein` · `Euclidean_distance_matrix` · `Exchange_matrix` · `Expander_graph` · `Frank_Harary` · `Frobenius_matrix` · `Fundamental_matrix_(computer_vision)` · `Fundamental_matrix_(linear_differential_equation)` · `Fuzzy_associative_matrix` · `GXL` · `Gamma_matrices` · `Gell-Mann_matrices` · `Generalized_permutation_matrix` · `Generator_matrix` · `Gordon_Royle` · `Gram_matrix` · `GraphML` · `Graph_(abstract_data_type)` · `Graph_(discrete_mathematics)` · `Graph_Modelling_Language` · `Graph_database` · `Graph_drawing` · `Graph_isomorphism` · [[Graph_theory]] · `Hadamard_matrix` · `Hamiltonian_matrix` · `Hankel_matrix` · `Hermitian_matrix` · `Hessenberg_matrix` · `Hessian_matrix` · `Hilbert_matrix` · `Hollow_matrix` · `Householder_transformation` · `Hurwitz-stable_matrix` · `Idempotent_matrix` · `Identity_matrix` · `If_and_only_if` · `Incidence_(graph)` · `Incidence_matrix` · `Integer_matrix` · `Introduction_to_Algorithms` · `Invertible_matrix` · `Involutory_matrix` · `Irregular_matrix` · `Isospectral` · `Jabotinsky_matrix` · `Jacobian_matrix_and_determinant` · `Jordan_normal_form` · `LCF_notation` · `Laplacian_matrix` · `Lehmer_matrix` · `Linear_Algebra_and_Its_Applications` · `Linear_independence` · `Linked_data` · `Locality_of_reference` · `Logical_matrix` · `Loop_(graph_theory)` · `MathWorld` · `Matrix_(mathematics)` · `Matrix_congruence` · `Matrix_exponential` · `Matrix_multiplication` · `Matrix_of_ones` · `Matrix_representation` · `Matrix_representation_of_conic_sections` · `Matrix_unit` · `Metzler_matrix` · `Michael_T._Goodrich` · `Minimal_polynomial_(linear_algebra)` · `Moment_matrix` · `Moore_matrix` · `Multigraph` · `Nauru_graph` · `Neighbourhood_(graph_theory)` · `Newick_format` · `Nilpotent_matrix` · `Nonnegative_matrix` · `Normal_matrix` · `Orthogonal_matrix` · `Pascal_matrix` · `Pat_Morin` · `Path_(graph_theory)` · `Pauli_matrices` · `Perfect_matrix` · `Permutation_matrix` · `Perron–Frobenius_theorem` · `Persymmetric_matrix` · `Polynomial_matrix` · `Precision_(statistics)` · `Projection_(linear_algebra)` · `Projection_matrix` · `Python_(programming_language)` · `Quaternionic_matrix` · `Random_matrix` · `Real_number` · `Redheffer_matrix` · `Roberto_Tamassia` · `Rotation_matrix` · `Routh–Hurwitz_matrix` · `Row_echelon_form` · `S-matrix` · `Seidel_adjacency_matrix` · `Self-similarity_matrix` · `Shift_matrix` · `Signature_matrix` · `Skew-Hermitian_matrix` · `Skew-symmetric_matrix` · `Skyline_matrix` · `Sparse_matrix` · `Spectral_gap` · `Spectral_graph_theory` · `Spectral_radius` · `Square_matrix` · `State-transition_matrix` · `Statistics` · `Stieltjes_matrix` · `Stochastic_matrix` · `Strongly_regular_graph` · `Substitution_matrix` · `Sylvester_matrix` · `Symmetric_group` · `Symmetric_matrix` · `Symplectic_matrix` · `Text_file` · `Thomas_H._Cormen` · `Toeplitz_matrix` · `Totally_positive_matrix` · `Trace_(linear_algebra)` · `Transformation_matrix` · `Triangular_matrix` · `Tridiagonal_matrix` · `Trivial_Graph_Format` · `Tutte_matrix` · `Two-graph` · `Unimodular_matrix` · `Unipotent` · `Unitary_matrix` · `Vandermonde_matrix` · `Vertex_(graph_theory)` · `Walsh_matrix` · `Weighing_matrix` · `Wronskian` · `XGMML` · `Z-matrix_(chemistry)` · `Z-matrix_(mathematics)` · `Zero_matrix` > Signal Processing concept · part of the Signal Processing Portal · movement IX · !09 解析 kaiseki.svg  !480 *Rendered from the live microsim (▶ motion).*  ## See it next [![Graph theory|200](Graph_theory_thumb.png)](Graph_theory) *→ [[Graph_theory|Graph theory]]*  --- Back to Signal Processing Portal · the room · Semiotic gateway ## What it is An adjacency matrix is a square matrix used to represent a finite graph, where the entry in row i and column j indicates whether (or with what weight) vertices i and j are connected by an edge. ## How it works / why it matters For a graph with n vertices the matrix is n×n; entry $A_{ij}$ is 1 (or the edge weight) when an edge joins vertex i to vertex j and 0 otherwise, and the matrix is symmetric for undirected graphs. In graph signal processing the adjacency matrix (or the closely related Laplacian) plays the role of a shift operator: its eigenvectors define a graph Fourier basis, so filtering and transforms generalize from regular time grids to arbitrary network structures. ## Signs & universals Instantiates: network · transformation · measurement — a matrix encoding of a network whose eigenstructure supports graph transforms. ## Related It is the core data structure of [[Graph_theory]] and underpins graph-based Algebraic signal processing, where a shift operator generates a signal model. It relates to [[Linear_algebra]] and Vector spaces through its eigen-decomposition, and its spectral use parallels the Discrete Fourier transform within Signal Processing.  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Adjacency_matrix) : [Wikitube](https://en.wikitube.io/wiki/Adjacency_matrix) ## Previous hub tags Tree parents: [[Graph_theory]] · [[Network_theory]]. Legacy hubs: none. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*