In graph theory, a walk-regular graph is a simple graph where the number of closed walks of any length ℓ {\displaystyle \ell } from a vertex to itself...

A continuous-time quantum walk (CTQW) is a quantum walk on a given (simple) graph that is dictated by a time-varying unitary matrix that relies on the...

In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is...

Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...

spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are...

walk on a regular lattice, where at each step the location jumps to another site according to some probability distribution. In a simple random walk,...

In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander...

In the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian...

edge-transitive, the Hoffmann graph is still 1-walk-regular (but not distance-regular). The characteristic polynomial of the Hoffman graph is equal to ( x − 4 )...

Shrikhande graph and the Hoffman graph are integral. A regular graph is periodic if and only if it is an integral graph. A walk-regular graph that admits...

In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether...

between two curves. The supersingular isogeny graphs are ℓ + 1 {\displaystyle \ell +1} -regular graphs, meaning that each vertex has exactly ℓ + 1 {\displaystyle...

In the mathematical discipline of graph theory, a graph C is a covering graph of another graph G if there is a covering map from the vertex set of C to...

In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors...

elements, the Cayley graph is a regular directed graph of degree r . {\displaystyle r.} Cycles (or closed walks) in the Cayley graph indicate relations...

In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges...

quantum walk search is a quantum algorithm for finding a marked node in a graph. The concept of a quantum walk is inspired by classical random walks, in which...

graphs Applications of label propagation algorithms, etc. New graph-based methods for NLP applications Random walk methods in graphs Spectral graph clustering...

computer science, graph traversal (also known as graph search) refers to the process of visiting (checking and/or updating) each vertex in a graph. Such traversals...

A graph database (GDB) is a database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data. A key...

of a directed graph, in which case it can be used to analyze how quickly random walks in the graph converge. The conductance of a graph is closely related...

the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly...

mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each...

function associated with a finite graph. It closely resembles the Selberg zeta function, and is used to relate closed walks to the spectrum of the adjacency...

nearest each vertex of the graph are congruent 17-sided polyhedra that tile space. Its edges lie on diagonals of the regular skew polyhedron, a surface...

introduced into the physics literature by Hans Bethe in 1935. In such a graph, each node is connected to z neighbors; the number z is called either the...

K6-minor-free graph is an apex graph Does a Moore graph with girth 5 and degree 57 exist? Do there exist infinitely many strongly regular geodetic graphs, or any...

In graph theory, the zig-zag product of regular graphs G , H {\displaystyle G,H} , denoted by G ∘ H {\displaystyle G\circ H} , is a binary operation which...

the eigenvalues of its adjacency matrix. For an r {\displaystyle r} -regular graph, these are real numbers in the interval [ − r , r ] {\displaystyle [-r...

A chart (sometimes known as a graph) is a graphical representation for data visualization, in which "the data is represented by symbols, such as bars...