*(Guest post by Thomas Klonowski)*

In class on 9/29/2010 we continued to concept of graphs.

First we were given a key for Default instances (cases where it is not specified):

- # of vertices = n
- #of edges = m

*Definitions discussed this lecture:*

**Path – **A sequence of vertices connected by edges. Repeated vertices are allowed.

- Good Examples:
- V
_{1}o——–oV_{2}——–0 V_{3} - V
_{1}o——->oV_{2}——–0 V_{3} - Bad Example:
- V
_{1}o——->oV_{2}<——-0 V_{3}

**Path Length **– Number of edges travelled

**Cycle** – A sequence of vertices connected by edges.

- You can have a path with only 1 vertice (Won’t use this in class)
- Symbolic representation:
_{1},V_{2},………V_{k-1}) where V_{k }= V_{1 }& (V_{1}, V_{i + 1}) Є E 1<= i <= k -1

**Directed Graph – **A graph with an asymmetrical relationship. I.e. Wikipedia articles. An article A may have a reference to an article B, but it does not necessarily mean article B has a reference to article A.

- Symbolic Representation: (u,v) Є E & (v, u)
**Not****Є**E - Examples: In class TV Host graph, Webpages on the internet.

**Undirected graph** – A graph with a symmetrical relationship. I.e. Facebook. In facebook in order to add someone, they must accept your request. This can be considered a “sub-set” of a Directed graph.

- Symbolic representation: (u,v) Є E <==> (v,u) Є E
- Graphic representation: u o————-o v(not u o——-> v)
- Examples: Airline route graph, routers (typically), Facebook.

*Concepts talked about:*

G = (V, E) where V is the vertices and E is the set of edges.

Graphs by default are undirected.

Simple path is a path with no repeated vertex.

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