1 / 9

Understanding Graph Representation: Edges, Sparse vs. Dense, and Space Complexity

This overview explores key concepts in graph algorithms, focusing on undirected graphs that are connected and have no parallel edges. It discusses the minimum and maximum edge counts in such graphs, differentiating between sparse and dense graphs. The representation methods of graphs, including adjacency matrices and adjacency lists, are examined, detailing their space requirements as functions of the number of vertices and edges. This foundational understanding is critical for efficiently designing and analyzing graph algorithms.

luther
Download Presentation

Understanding Graph Representation: Edges, Sparse vs. Dense, and Space Complexity

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Graph Algorithms Representing Graphs Design and Analysis of Algorithms I

  2. Graphs

  3. Consider an undirected graph that has vertices, no parallel edges, and is connected (i.e., “in one piece”). What is the minimum and maximum number of edges that the graph could have, respectively? and

  4. Sparse vs. Dense Graphs

  5. The Adjacency Matrix

  6. How much space does an adjacency matrix require, as a function of the number of vertices and the number of edges?

  7. Adjacency Lists

  8. How much space does an adjacency list representation require, as a function of the number of vertices and the number of edges?

  9. Adjacency Lists

More Related