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In graph theory, a loop (also called a self-loop or a buckle) is an edge that connects a vertex to itself. A simple graph contains no loops. Depending on the context, a graph or a multigraph may be defined so as to either allow or disallow the presence of loops (often in concert with allowing or disallowing multiple edges between the same ...
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
The degree or valency of a vertex is the number of edges that are incident to it, where a loop is counted twice. The degree of a graph is the maximum of the degrees of its vertices. In an undirected simple graph of order n, the maximum degree of each vertex is n − 1 and the maximum size of the graph is n(n − 1) / 2 .
Simple graphs: Graphs without self-loops or multi-edges. Multi-edge graphs: Graphs allowing multiple edges between the same pair of nodes. Loopy graphs: Graphs that include self-loops (edges connecting a node to itself). Directed graphs: Models with specified in-degrees and out-degrees for each node. Undirected graphs: Models that consider the ...
simple 1. A simple graph is a graph without loops and without multiple adjacencies. That is, each edge connects two distinct endpoints and no two edges have the same endpoints. A simple edge is an edge that is not part of a multiple adjacency. In many cases, graphs are assumed to be simple unless specified otherwise. 2.
Where graphs are defined so as to allow multiple edges and loops, a graph without loops or multiple edges is often distinguished from other graphs by calling it a simple graph. [1] Where graphs are defined so as to disallow multiple edges and loops, a multigraph or a pseudograph is often defined to mean a "graph" which can have multiple edges. [2]
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called arcs ), with each edge directed from one vertex to another, such that following those directions will never form a closed loop.
A simple graph contains no double edges or loops. [1] The degree sequence is a list of numbers in nonincreasing order indicating the number of edges incident to each vertex in the graph. [2] If a simple graph exists for exactly the given degree sequence, the list of integers is called graphic. The Havel-Hakimi algorithm constructs a special ...