graph on a table (concrete structure. on a Relational Mode/SQL for example, not a very good implementation) or on abstract data structures. Apart from the traditional graph implemataion (Ajacency Matrix and Ajacency List)
The main problem in processing a graph database represented by a table is the frequent accessing the database for checking the adjacency between the graph nodes.
The Relation model/SQL are not sufficiently expressive to implement the majority of the standard [graph] algorithms.
Consider the graph on a table http://wiki.c2.com/?GraphAlgorithmsWithTables
need to consider the following aspect on a graph