Page 74 - Data Structures Interactive Book
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8.2.3 Comparison of Representations
Choosing between adjacency matrices and adjacency lists depends on the graph’s
density and the operations required:
• Adjacency Matrix:
o Advantages: Constant-time edge lookup, simple implementation.
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o Disadvantages: High memory usage ( ( )), inefficient for sparse graphs.
• Adjacency List:
o Advantages: Efficient memory usage ( ( + )), faster traversal for sparse
graphs.
o Disadvantages: Slower edge lookup, as it requires searching through lists.
Example: Comparing Edge Lookup
In the adjacency matrix, checking for an edge is immediate. In the adjacency list, it
requires iterating through the list of neighbors, which can be slower if the vertex has many
connections.
8.3 Graph Traversal Techniques
Traversal in graphs refers to the systematic process of visiting all vertices and edges in
a graph. Unlike trees, where traversal is relatively straightforward due to their hierarchical
and acyclic nature, graphs can be more complex because they may contain cycles,
disconnected components, and multiple paths between vertices. Traversal algorithms are
fundamental because they form the basis for solving many graph-related problems, such as
connectivity, shortest paths, cycle detection, and network analysis. Two of the most widely
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