In graph theory the complement or inverse of a graph G is a graph H on the same vertices such that two vertices of H are adjacent if and only if they are not adjacent in G. That is, to find the complement of a graph, you fill in all the missing edges, and remove all the edges that were already there. It is not the set complement of the graph; only the edges are complemented. In mathematics and computer science, graph theory studies the properties of graphs. ... In mathematics, philosophy, logic and technical fields that depend on them, iff is used as an abbreviation for if and only if. It is often, not always, written italicized: iff. ... In set theory and other branches of mathematics, two kinds of complements are defined, the relative complement and the absolute complement. ...
A quiver is sometimes said to be simply a directed graph, but in practice it is a directed graph with vector spaces attached to the vertices and linear transformations attached to the arcs.
In a weighted graph or digraph, each edge is associated with some value, variously called its cost, weight, length or other term depending on the application; such graphs arise in many contexts, for example in optimal routing problems such as the traveling salesman problem.
Every graph gives rise to a matroid, but in general the graph cannot be recovered from its matroid, so matroids are not truly generalizations of graphs.
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