# Category: Extensions and generalizations of graphs

Bidirected graph
In the mathematical domain of graph theory, a bidirected graph (introduced by ) is a graph in which each edge is given an independent orientation (or direction, or arrow) at each end. Thus, there are
Multigraph
In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges), that is, edges that have the same end nodes. Thus
Two-graph
In mathematics, a two-graph is a set of (unordered) triples chosen from a finite vertex set X, such that every (unordered) quadruple from X contains an even number of triples of the two-graph. A regul
Gain graph
A gain graph is a graph whose edges are labelled "invertibly", or "orientably", by elements of a group G. This means that, if an edge e in one direction has label g (a group element), then in the othe
Ancestral graph
In statistics and Markov modeling, an ancestral graph is a type of mixed graph to provide a graphical representation for the result of marginalizing one or more vertices in a graphical model that take
Rooted graph
In mathematics, and, in particular, in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. Both directed and undirected versions of rooted graphs have been
Quantum graph
In mathematics and physics, a quantum graph is a linear, network-shaped structure of vertices connected on edges (i.e., a graph) in which each edge is given a length and where a differential (or pseud
Graph labeling
In the mathematical discipline of graph theory, a graph labelling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. Formally, given a graph G = (
Ordered graph
An ordered graph is a graph with a total order over its nodes. In an ordered graph, the parents of a node are the nodes that are adjacent to it and precede it in the ordering. More precisely, is a par
Signed graph
In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is
Voltage graph
In graph theory, a voltage graph is a directed graph whose edges are labelled invertibly by elements of a group. It is formally identical to a gain graph, but it is generally used in topological graph