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The Hamiltonian path problem is a topic discussed in the fields of complexity theory and graph theory. It decides if a directed or undirected graph, G, contains a Hamiltonian path, a path that visits every vertex in the graph exactly once. The problem may specify the start and end of the path, in which case the starting vertex s and ending ...
The shortest path problem can be defined for graphs whether undirected, directed, or mixed. Here it is defined for undirected graphs; for directed graphs the definition of path requires that consecutive vertices be connected by an appropriate directed edge. [2] Two vertices are adjacent when they are both incident to a common edge.
Circulant graph. The Paley graph of order 13, an example of a circulant graph. In graph theory, a circulant graph is an undirected graph acted on by a cyclic group of symmetries which takes any vertex to any other vertex. It is sometimes called a cyclic graph, [1] but this term has other meanings.
The Heawood graph is bipartite. In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets and , that is, every edge connects a vertex in to one in . Vertex sets and are usually called the parts of the graph.
e. In the mathematical field of graph theory, the Erdős–Rényi model refers to one of two closely related models for generating random graphs or the evolution of a random network. These models are named after Hungarian mathematicians Paul Erdős and Alfréd Rényi, who introduced one of the models in 1959. [1][2] Edgar Gilbert introduced the ...
Triangle-free graph. In the mathematical 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 defined as graphs with clique number ≤ 2, graphs with girth ≥ 4, graphs with no induced 3-cycle, or locally independent graphs.
It is a directed or undirected graph consisting of vertices, which represent concepts, and edges, which represent semantic relations between concepts, [1] mapping or connecting semantic fields. A semantic network may be instantiated as, for example, a graph database or a concept map .
v. t. e. A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables. They are commonly used in probability theory, statistics —particularly Bayesian statistics —and machine learning.
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