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The 29 pages that link to Incidence matrix, each with the reason it gives.

• Directed graphRelated: An oriented incidence matrix can encode each edge's source and destination.

• Incidence geometryRelated: It encodes point-line incidences in a form suited to algebraic analysis.

• Graph (discrete mathematics)Related: It encodes the two basic graph sets and their incidences.

• Edge (graph theory)Related: Each edge is represented by its relationship to the graph's vertices.

• Vertex (graph theory)Related: It encodes vertex-edge membership in a matrix rather than as a drawing.

• MultigraphRelated: Separate columns preserve the identity of parallel edges.

• Directed acyclic graphRelated: It offers an algebraic representation of the directed edges in an acyclic graph.

• HypergraphRelated: Its rows and columns encode vertices and hyperedges, exposing their membership pattern.

• Simple graphRelated: It represents the vertex-edge relationships of a simple graph.

• Line graphRelated: Multiplying incidence data reveals which pairs of original edges meet.

• IncidenceRelated: Its entries encode incidences between two classes of geometric objects.

• Flow conservationRelated: Multiplying by this matrix expresses vertex balance as linear equations.

• Path graphRelated: It represents each path edge as incident to neighboring vertices.

• Petri netRelated: Its entries summarize arc effects and support algebraic analysis of net behavior.

• Undirected graphRelated: It encodes undirected edge endpoints directly, including in multigraphs.

• Finite geometryRelated: It turns finite geometric incidence into an object studied by linear algebra and combinatorics.

• Simplicial complexRelated: Boundary incidence between simplices can be encoded in matrices.

• Handshaking lemmaRelated: Its entries encode the incidences whose total gives the degree sum.

• Circulation problemRelated: Its columns encode the conservation equations used in linear formulations of circulation.

• Regular graphRelated: Its structure captures how a fixed degree is distributed across every vertex.

• Degree matrixRelated: Summing incidence information by vertex can recover degrees, subject to convention.

• Spectral graph theoryRelated: Factoring the Laplacian through this matrix connects spectra to graph structure.

• Kirchhoff's theoremRelated: Its factorization of the Laplacian links tree counts to determinants.

• Laplacian matrixRelated: For an oriented graph, the Laplacian factors as the incidence matrix times its transpose.

• Erdős–Gallai theorem (degree sequences)Related: It offers another representation for checking a proposed graph’s vertex degrees.

• Tellegen's theoremRelated: Its transpose relates node potentials to branch voltages, while it also encodes current conservation.