W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph,...

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W5L1. Introduction to Graph Theory Reference book: Discrete Mathematics. K.Rosen

Transcript of W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph,...

Page 1: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

W5L1.Introduction to Graph Theory

Reference book: Discrete Mathematics. K.Rosen

Page 2: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Types of graphs

Page 3: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Types of graphs

Page 4: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Directed graphs

Page 5: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Summary of graph types

Page 6: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Real life applications

Page 7: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Real life applications

Page 8: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Real life applications

Page 9: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Real life applications

Page 10: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Real life applications

Page 11: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Real life applications

Page 12: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Basic concepts

Page 13: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Example

Page 14: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

How to calculate?

Page 15: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

In-Out degree

Page 16: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Example

Page 17: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Some special graphs

Page 18: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Special graphs

Page 19: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Applications of special graphs

Page 20: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Applications of special graphs

Page 21: W5L1.Intro to graphs · an edge if team a beats team b. This graph is a simple directed graph, containing no loops or multiple directed edges (because no two teams play each other

Graph Drawing by Force-directed Placement Jana Ludolph.

Graph Drawing by Force-directed Placement Jana Ludolph.

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Graph II MST, Shortest Path. Graph Terminology Node (vertex) Edge (arc) Directed graph, undirected graph Degree, in-degree, out-degree Subgraph Simple.

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Graph Signal Processing on directed graph for modelling and … · 2019-05-06 · Graph Signal Processing on directed graph for modelling and learning Pierre Borgnat DR CNRS – Laboratoire

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