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This lesson contains approximately 25 minutes of video content.

Sets

Graphs

Some types of graphs and their properties

How do graphs prove useful?

Questions

QIntroduction to Graphs, Q1

This question is ungraded.

Given the following graph,

what are the corresponding vertex v and edge e sets?

`v:{A,B,C,D,E,F} e:{(A,B),(B,D),(B,E),(D,C),(E,F)}`

`v:{A,B,C,D,E,F} e:{(A,B),(B,D),(C,D),(E,B)}`

`v:{A,B,C,D,E} e:{(A,B),(B,D),(B,E),(D,C)}`

`v:{F} e:{(A,B),(B,D),(B,E),(D,C)}`

Practice question: try as many times as you like

QIntroduction to Graphs, Q2

This question is ungraded.

Given the following directed graph,

what are the corresponding vertex v and edge e sets?

`v:{A,B,C,D} e:{(A,B),(B,C),(B,D),(C,D),(D,B)}`

`v:{A,B,C,D} e:{(A,B),(B,C),(C,D),(D,B)}`

`v:{A,B,C,D} e:{(A,B),(B,D),(C,B),(C,D),(D,B)}`

`v:{A,B,C,D} e:{(B,A),(C,B),(B,D),(D,C),(D,B)}`

Practice question: try as many times as you like

QIntroduction to Graphs, Q3

This question is ungraded.

What is the difference between a simple graph and a multigraph?

Simple graphs are directed; multigraphs are undirected.

Simple graphs consist of a finite number of vertices, whereas multigraphs allow infinite.

Simple graphs do not allow intersecting edges, whereas multigraphs do.

Simple graphs only allow one edge per vertex pair, whereas multigraphs allow several edges per vertex pair.

Practice question: try as many times as you like

QIntroduction to Graphs, Q4

This question is ungraded.

How many vertices are required for a cycle in a simple graph?

`1`

`2`

`3`

`4`

Practice question: try as many times as you like

QIntroduction to Graphs, Q5

This question is ungraded.

Suppose we are modeling a social network of friends as an undirected graph whose vertices are people and edges denote friendship, as mentioned in the lecture video. Given the following undirected graph,

which of the choices below make an incorrect statement about the graph?

`A` and `B` are friends.

`A` and `B` have the same number of friends.

`A` and `C` are mutual friends (share a common friend).

`B` and `D` have 2 mutual friends (friends in common).

Practice question: try as many times as you like

An introduction to graphs

Sets

Graphs

Some types of graphs and their properties

How do graphs prove useful?

Questions

1

QIntroduction to Graphs, Q1

2

QIntroduction to Graphs, Q2

3

QIntroduction to Graphs, Q3

4

QIntroduction to Graphs, Q4

5

QIntroduction to Graphs, Q5