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Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter sense, geometric graph theory studies combinatorial and geometric properties of geometric graphs, meaning graphs drawn in the Euclidean plane with possibly intersecting straight-line edges, and topological graphs, where the edges are ...
Geometric graph theory is a branch of graph theory. It concerns straight-line embeddings of graphs in geometric spaces and graphs defined from configurations in a ...
In graph theory, a random geometric graph (RGG) is the mathematically simplest spatial network, namely an undirected graph constructed by randomly placing N nodes in some metric space (according to a specified probability distribution) and connecting two nodes by a link if and only if their distance is in a given range, e.g. smaller than a certain neighborhood radius, r.
In set theory and graph theory, denotes the set of n-tuples of elements of , that is, ordered sequences of elements that are not necessarily distinct. In the edge ( x , y ) {\displaystyle (x,y)} directed from x {\displaystyle x} to y {\displaystyle y} , the vertices x {\displaystyle x} and y {\displaystyle y} are called the endpoints of the ...
Spectral graph theory is the branch of graph theory that uses spectra to analyze graphs. See also spectral expansion. split 1. A split graph is a graph whose vertices can be partitioned into a clique and an independent set. A related class of graphs, the double split graphs, are used in the proof of the strong perfect graph theorem.
4.1 Graph theory. 4.2 Order theory. 5 Dynamical systems. 6 Geometry. ... Frostman's lemma (geometric measure theory) Malliavin's absolute continuity lemma; Topology
Discrete geometry has a large overlap with convex geometry and computational geometry, and is closely related to subjects such as finite geometry, combinatorial optimization, digital geometry, discrete differential geometry, geometric graph theory, toric geometry, and combinatorial topology.
A spatial network (sometimes also geometric graph) is a graph in which the vertices or edges are spatial elements associated with geometric objects, i.e., the nodes are located in a space equipped with a certain metric.