Lec 61 - Representation of graphs
IIT Madras - B.S. Degree Programme・2 minutes read
Graphs and problems on graphs were discussed, focusing on topics like reachability, graph coloring, and vertex cover. The text explores mathematical concepts related to graphs, including the use of adjacency matrices to represent graphs and determine reachability between vertices.
Insights
- Graphs consist of vertices and edge relations, with paths defined by connected edges. Representing graphs mathematically through an adjacency matrix simplifies computations, enabling efficient determination of reachability and connectivity between vertices.
- The choice between an adjacency matrix and an adjacency list impacts algorithm efficiency. While an adjacency matrix simplifies representation, it may be less efficient for specific tasks like finding incoming edges in directed graphs. Conversely, an adjacency list is advantageous for graphs with low degrees, reducing time complexity proportional to node degree. Both representations facilitate systematic computations and exploration strategies like breadth-first and depth-first searches in graph theory.
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Recent questions
What is a graph in mathematics?
A graph comprises vertices and edge relations.
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