In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected...

important in the study of dense graphs. Graphons arise both as a natural notion for the limit of a sequence of dense graphs, and as the fundamental defining...

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...

which gives a linear run-time for dense graphs. There are other algorithms that work in linear time on dense graphs. If the edge weights are integers...

Bruijn graph Dense graph Dipole graph Directed acyclic graph Directed graph Distance regular graph Distance-transitive graph Edge-transitive graph Interval...

In graph theory and computer science, a dense subgraph is a subgraph with many edges per vertex. This is formalized as follows: let G = (V, E) be an undirected...

In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it...

size of a clique in dense graphs. If a graph has sufficiently many edges, it must contain a large clique. For instance, every graph with n {\displaystyle...

certain properties of random graphs can be applied to dense graphs like counting the copies of a given subgraph within graphs. Endre Szemerédi proved the...

various graphs H {\displaystyle H} . By extending the homomorphism density to graphons, which are objects that arise as a limit of dense graphs, the graph homomorphism...

In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a...

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect...

In graph theory, the graph bandwidth problem is to label the n vertices vi of a graph G with distinct integers ⁠ f ( v i ) {\displaystyle f(v_{i})} ⁠ so...

n-vertex t-biclique-free graph has O(n2 − 1/t) edges, significantly fewer than a dense graph would have. Conversely, if a graph family is defined by forbidden...

graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge. The neighbourhood of a vertex v in a graph G...

vertices in a dense graph such that every small subset of vertices has many common neighbors. It is a useful tool to embed a graph into another graph with many...

area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently...

been explored. As graphs become more dense, this redundancy becomes more prevalent, causing computation time to increase; as graphs become more sparse...

problem. Although dense graphs can have a number of edges proportional to the square of the number of vertices, locally linear graphs have a smaller number...

science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within...

In the mathematical field of graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices of...

Many interesting properties of dense graphs can be tested using query complexity that depends only on ε and not on the graph size n. However, the query complexity...

⁡ V ) {\displaystyle O(E\log V)} for sparse graphs and O ( V 2 ) {\displaystyle O(V^{2})} for dense graphs. This is as fast as Prim's algorithm for an...

Balázs Szegedy for characterizing subgraph multiplicity in sequences of dense graphs. 2015: Francisco Santos Leal for a counter-example of the Hirsch conjecture...

A scene graph is a general data structure commonly used by vector-based graphics editing applications and modern computer games, which arranges the logical...

decision problem decision tree decomposable searching problem degree dense graph depoissonization depth depth-first search (DFS) deque derangement descendant...

the structure of dense graphs; he was the first to prove detailed results about the phase transition in the evolution of random graphs; he proved that...

an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer...

Floyd-Warshall algorithm, the constants involved matter quite a lot. When a graph is dense (i.e., | E | ≈ | V | 2 {\displaystyle |E|\approx |V|^{2}} ), the Floyd-Warshall...

graphs, a giant component is a connected component whose fraction of the overall number of vertices is bounded away from zero. In sufficiently dense graphs...