Lecture 37: Graphs

Michael J. Bannister and Kim BrucePomona College, Fall 2015

Announcements

• Reading: Bailey Chapter 16• Assignment 12: Driving Directions• Lab 12: Graph Search

Examples of Graphs

• Communication networks• Transportation networks• Social networks• Biological interaction networks• Matching graphs• and many more...

Things to do with graphs

• Find shortest/“cheapest” routes• Minimize cost for connecting a network• Maximize communication throughput• Answer sociological queries• Match ads to viewers• Cure cancer• Visualize• Have fun!

Definitions

• A graph G is a pair (V,E) such that• V is a (finite) set of vertices (aka nodes)• E is a set of (ordered) pairs of vertices called edges

Directed vs. Undirected

• Undirected graphs: Edges are symmetric– A roads are two way roads

• Directed graphs: Edges are directed from theirsource to their destinations– Some roads may be one way roads

• (Example on board)

Graph Terms

• incident• adjacent• degree (in and out)• path• path length• cycle

• simple path• simple cycle• self loop• acyclic graph (tree)• simple graph• Connected• Strongly connected

(on board)

Digital Representations

• Adjacency Matrix– Store graph as a n× n matrix of bool

• Adjacency List– For each vertex store a list of (in and out)

neighbors

(details on board)