LEDA Graph Win

Emanuele AltieriOctober 31, 2000

Vertices and edges

Multiple edges. Loops

Undirected Graph

Directed Graph

Simple Graph

The graph doesn’t have multiple edges

Complete and Bipartite Graphs

Complete Graph

All of the nodes in the Graph are

connected each other.

Bipartite GraphThe nodes in the graph are

divided into two classes. Edges exist only between nodes of

different classes.

Path in Undirected Graphs

Simple path. The sub-graph is connected and has two first-degree nodes (0 and 6). The

other nodes of the sub-graph are second-degree.

Path in Directed Graphs

Simple path. The sub-graph is connected and has one zero-indegree source node (0), and one zero-outdegree destination node (5). The other nodes of the sub-graph are second-degree

(1 in/out degree).

Hamilton Path in Undirected Graphs

The subgraph is a simple path which spans all of the nodes in

the graph

Hamilton Path in Directed Graphs

The subgraph is a simple path which spans all of the nodes in

the graph

Cycle in Undirected Graphs

The bold subgraph above is connected and its vertices are

second-degree.

Cycle in Directed Graphs

The subgraph is connected and its vertices are 1 indegree and 1

outdegree

Hamilton Cycle in Undirected Graphs

The subgraph is a simple cycle which includes all of the nodes

in the graph

Hamilton Cycle in Directed Graphs

The subgraph is a simple cycle which includes all of the nodes

in the graph

Cyclic and Acyclic Digraphs

Cyclic GraphThe graph contains

cycles

Acyclic GraphThe graph does not contain

cycles

Tree

The subgraph is a path which is a tree

Forest

1

5

4

8

10

7

2

6

3

11

9

Strongly Connected Digraph

The graph is connected. All of the nodes in the graph are

strongly connected each other.