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

O(m)
replace
O(1)
insertVertex, insert Edge, removeEdge,
O(1)
removeVertex
O(m)
Details for selected methods of the graph ADT are as follows:
• Methods vertices() and edges() are implemented by calling
V.iterator() and E.iterator(), respectively.
• Methods incidentEdges and areAdjacent all take O(m) time,
since to determine which edges are incident upon a vertex v we must inspect all
edges.
• Since the collections V and E are lists implemented with a doubly linked
list, we can insert vertices, and insert and remove edges, in O(1) time.
• The update method removeVertex(v) takes O(m) time, since it requires
that we inspect all the edges to find and remove those incident upon v.
Thus, the edge list representation is simple but has significant limitations.
13.2.2 The Adjacency List Structure
The adjacency list structure for a graph G adds extra information to the edge list
structure that supports direct access to the incident edges (and thus to the adjacent
vertices) of each vertex. This approach allows us to use the adjacency list structure
to implement several methods of the graph ADT much faster than what is possible
with the edge list structure, even though both of these two representations use an
amount of space proportional to the number of vertices and edges in the graph. The
adjacency list structure includes all the structural components of the edge list
structure plus the following:
• A vertex object v holds a reference to a collection I(v), called the
incidence collection of v, whose elements store references to the edges incident
on v.
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