If the pair v , w are ordered then the graph is directed , if the pair is unordered then the graph is undirected . A graph contains a cycle if for some point you can traverse the graph on distinct edges and return to the starting point. The graph is acyclic if it does not have a cycle. A tree is an acyclic graph. A graph is connected if there is a path from any vertex to any other vertex.
Definitions are the same whether the graph is directed or undirected.
Graph Representation Often times represent a graph by indicating the set of vertices adjacent to each vertex. This representation can be formed given the set of edges for a graph. Adjacency sets - maintain an array of sets. Fig 10.14 in Kruse. In an undirected graph only need to use half of the table.