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For undirected planar graphs, one way to construct an arc diagram with at most two semicircles per edge is to subdivide the graph and add extra edges so that the resulting graph has a Hamiltonian cycle (and so that each edge is subdivided at most once), and to use the ordering of the vertices on the Hamiltonian cycle as the ordering along the ...
A loop is an edge that joins a vertex to itself. Graphs as defined in the two definitions above cannot have loops, because a loop joining a vertex to itself is the edge (for an undirected simple graph) or is incident on (for an undirected multigraph) {,} = {} which is not in {{,},}. To allow loops, the definitions must be expanded.
A directed graph is weakly connected (or just connected [9]) if the undirected underlying graph obtained by replacing all directed edges of the graph with undirected edges is a connected graph. A directed graph is strongly connected or strong if it contains a directed path from x to y (and from y to x) for every pair of vertices (x, y).
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).
A numerical value, assigned as a label to a vertex or edge of a graph. The weight of a subgraph is the sum of the weights of the vertices or edges within that subgraph. weighted graph A graph whose vertices or edge s have been assigned weight s. A vertex-weighted graph has weights on its vertices and an edge-weighted graph has weights on its edges.
The different types of edge in a bidirected graph. In the mathematical domain of graph theory, a bidirected graph (introduced by Edmonds & Johnson 1970) [1] is a graph in which each edge is given an independent orientation (or direction, or arrow) at each end. Thus, there are three kinds of bidirected edges: those where the arrows point outward ...
A chart pattern or price pattern is a pattern within a chart when prices are graphed. In stock and commodity markets trading, chart pattern studies play a large role during technical analysis. When data is plotted there is usually a pattern which naturally occurs and repeats over a period. Chart patterns are used as either reversal or ...
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 ...