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Graph Algorithms. Representing Graphs. Design and Analysis of Algorithms I. Graphs. 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 . - PowerPoint PPT Presentation
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Graph AlgorithmsRepresenting Graphs
Design and Analysis of Algorithms I
Tim Roughgarden
Graphs
and
𝑛−1 and 𝑛2
𝑛 and 2𝑛
𝑛 and 𝑛𝑛
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?
Tim Roughgarden
Sparse vs. Dense Graphs
Tim Roughgarden
The Adjacency Matrix
𝜃(𝑛)𝜃(𝑚)𝜃(𝑚+𝑛)𝜃(𝑛2)
How much space does an adjacency matrix require, as a function of the number of vertices and the number of edges?
Tim Roughgarden
Adjacency Lists
𝜃(𝑛)𝜃(𝑚)𝜃(𝑚+𝑛)𝜃(𝑛2)
How much space does an adjacency list representation require, as a function of the number of vertices and the number of edges?
Tim Roughgarden
Adjacency Lists
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