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In mathematics, an unordered pair or pair set is a set of the form {a, b}, i.e. a set having two elements a and b with no particular relation between them, where {a, b} = {b, a}. In contrast, an ordered pair (a, b) has a as its first element and b as its second element, which means (a, b) ≠ (b, a).
In computer 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 mathematics. A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points ), together with a set of unordered pairs of these ...
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points ) which are connected by edges (also called arcs , links or lines ).
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).
r : E → {{x,y} : x, y ∈ V}, assigning to each edge an unordered pair of endpoint nodes. Some authors allow multigraphs to have loops, that is, an edge that connects a vertex to itself, [2] while others call these pseudographs, reserving the term multigraph for the case with no loops. [3]
A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...
Unordered pair, or pair set, in mathematics and set theory; Ordered pair, or 2-tuple, in mathematics and set theory; Pairing, in mathematics, an R-bilinear map of modules, where R is the underlying ring; Pair type, in programming languages and type theory, a product type with two component types; Topological pair, an inclusion of topological spaces
In mathematics, an ordered pair, denoted (a, b), is a pair of objects in which their order is significant. The ordered pair ( a , b ) is different from the ordered pair ( b , a ), unless a = b . In contrast, the unordered pair , denoted { a , b }, always equals the unordered pair { b , a }.