Graph Concepts Elif Tosun 252a-aa (All graphics created by using demo/graphwin/gw*)

Vertices, Edges

Multiple Edges, Loops The blue edges are multiple edges. Red edge shows a loop.

Undirected Graph There are no directions, i.e arrows in the graph, so it is undirected

Directed Graph - Digraph Each edge has a direction assigned to it. So it is a digraph (directed graph).

Simple Graph A graph with no loops or multiple edges.

Example of Graphs, MultiGraphs A simple graph A multi-graph

Complete Graph Complete graph on 5 vertices Complete graph on 6 vertices

Bipartite Graph The graph can be displayed as two disjoint sets of nodes. All edges leave one set of nodes and are directed to the other set of nodes.

Path in an undirected graph A path is a series of nodes. In this case, it is 5, 4, 0, 1, 3.

Path in a directed graph A path on a directed graph. Where you start and where you end is important. 5, 4, 0, 1, 3

Hamilton Path in an undirected graph A path that visits all nodes in an undirected graph.

Hamilton Path in a directed graph A path that visits all nodes in a digraph.

Cycle in an undirected graph A path that ends where it begins. The blue set of edges show one of the paths in the graph.

Cycle in a directed graph Blue set of edges show the only directed cycle in the graph.

Hamilton Cycle in an undirected graph A cycle that visits all the nodes of the graph.

Hamilton Cycle in a digraph A directed cycle that visits all the nodes of a graph.

Cyclic and Acyclic graph A cyclic graph An acyclic graph

Tree A graph that’s a tree. Each edge is directed downward and there is a root which is the root labeled 0.

Forest A set of trees. Disconnected.

Bi-connected Graph A biconnected graph where biconnectivity refers to the underlying graph, since it is term only defined for undirected graphs. It is biconnected since it has no articulation(cut) points.