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A more space-efficient way to implement a sparsely connected graph is to
use an adjacency list. In an adjacency list implementation, we keep a
master list of all the vertices in the Graph object and each vertex
object in the graph maintains a list of the other vertices that it is
connected to. In our implementation of the Vertex class we will use
a dictionary rather than a list, where the dictionary keys are the
vertices and the values are the weights. Figure 4
illustrates the adjacency list representation for the graph in
Figure 2.

The advantage of the adjacency list implementation is that it allows us
to compactly represent a sparse graph. The adjacency list also allows us
to easily find all the links that are directly connected to a particular
vertex.