Graphs


















Draw an example of a graph on the board.
(graph1.pdf)

	V = { a, b, c, d, e }
	E = { {a,b}, {a,c}, {a,e}, {b,c}, {c,d}, {c,e}, {d,e} }

	a---e
	|\  |\
	| \ | d
	|  \|/
	b---c

What's a Graph?

	1. Set of nodes V
	2. Set of edges E (pairs of nodes)

What's an Undirected Graph?

	edges are bi-directional

What's a Directed Graph (digraph)?

	edges can be traversed in only one direction


















Graph Applications

Why are graphs so awesome?

	They can be used to model the real world and
	provide solutions to real-world problems.

Road Maps (google maps)

	Nodes are cities.
	Edges are roads.
	Find the best route to a destination.

Erdos-Bacon Number (Wikipedia)

	Nodes are people.
	Edges are collaborations.
	Find out how close you are to other people.

Project 5


















Graph Terminology

Classwork

You may work with a partner.
Answer the questions about the undirected graph.
(graph1.pdf)

	a---e
	|\  |\
	| \ | d
	|  \|/
	b---c

List the simple paths from node a to node c.

What's the length of the path ( a, b, c, d ) ?

What's the length of the path ( d, e, c, b, a, c ) ?

Does the graph have any paths with length 0?


















Classwork

You may work with a partner.
Answer the questions about the undirected graph.
(graph1.pdf)

	a---e
	|\  |\
	| \ | d
	|  \|/
	b---c

Is the path ( a, b, c, d, e ) a cycle?

Is the path ( e, d, c, a, e ) a cycle?

Is the path ( a, b, a ) a cycle?

Is the path ( a, e, d, c, d, e, a ) a cycle?

Is the graph a Cyclic graph?
Is the graph an Acyclic graph?


















Connected Graphs

What's a Connected graph?

	A graph with a path between every pair of nodes.

What's a Connected Component?

	A subset of the nodes in a graph such that
	there is a path between every pair of nodes.

What's a Strongly Connected directed graph?

	A graph with a path from x to y
	and also a path from y to x
	for every pair of nodes x,y in the graph.

What's a Strongly Connected Component of a directed graph?

	A subgraph that is strongly connected.