Representing Graphs

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Adjacency List

In graph theory, an adjacency list is the representation of all edges or arcs in a graph as a list.

Representation

The graph pictured above has this adjacency list representation:
a	adjacent to	b,c
b	adjacent to	a,c
c	adjacent to	a,b

If the graph is undirected, every entry is a set of two nodes containing the two ends of the corresponding edge; if it is directed, every entry is a tuple of two nodes, one denoting the source node and the other denoting the destination node of the corresponding arc. Typically, adjacency lists are unordered.

One difficulty with the adjacency list structure is that it has no obvious place to store data associated with the edges of a graph, such as the lengths or costs of the edges. To remedy this, some algorithms texts such as that of Goodrich and Tamassia advocate a more object oriented variant of the adjacency list structure, sometimes called an incidence list, which stores for each vertex a list of objects representing the edges incident to that vertex. To complete the structure, each edge must point back to the two vertices forming its endpoints. The extra edge objects in this version of the adjacency list cause it to use more memory than the version in which adjacent vertices are listed directly, but are a convenient location to store additional information about each edge.