Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

vertices and m edges, an edge list or adjacency list representation uses O(n + m)
space, whereas an adjacency matrix representation uses O(n 2 ) space.
13.2.1 The Edge List Structure
The edge list structure is possibly the simplest, though not the most efficient,
representation of a graph G. In this representation, a vertex v of G storing an
element o is explicitly represented by a vertex object. All such vertex objects are
stored in a collection V, such as an array list or node list. If V is an array list, for
example, then we naturally think of the vertices as being numbered.
Vertex Objects
The vertex object for a vertex v storing element o has instance variables for:
• A reference to o.
• A reference to the position (or entry) of the vertex-object in collection V.
The distinguishing feature of the edge list structure is not how it represents
vertices, however, but the way in which it represents edges. In this structure, an
edge e of G storing an element o is explicitly represented by an edge object. The
edge objects are stored in a collection E, which would typically be an array list or
node list.
Edge Objects
The edge object for an edge e storing element o has instance variables for:
• A reference to o.
• References to the vertex objects associated with the endpoint vertices of e.
• A reference to the position (or entry) of the edge-object in collection E.
Visualizing the Edge List Structure
We illustrate an example of the edge list structure for a graph G in Figure 13.3.
Figure 13.3: (a) A graph G; (b) schematic
representation of the edge list structure for G. We
visualize the elements stored in the vertex and edge
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