State the number of vertices and edges for each of the following networks:
Determine if the following networks are valid:
Consider the following network:
Are there more vertices or more edges?
Is this property true for all networks?
For the following network, list the pairs of vertices that are connected by an edge.
For the following network, there is an edge from A to B. List the remaining edges.
Determine whether the following statements are true or false in regard to networks:
There is always at least one vertex.
There is always at least one edge.
All vertices must be connected to every other vertex by edges.
An edge can start and end at the same vertex.
Edges always start and end at vertices.
An edge can connect three vertices together.
State whether the following are directed or undirected networks:
State whether the following are best represented by an undirected or directed network:
Which countries border each other
The results of an elimination-style sports tournament
The animals that different animals eat
Your parents and their ancestors
Ways to get from one classroom to another at school
How parts of the body are connected
How many loops are in the following networks:
State whether the following networks contain a pair of vertices that have multiple edges between them:
State whether the following networks are simple:
State the two changes required to make the following network simple:
For each of the following networks, state a valid walk that crosses each vertex once:
State a path that satisfies the given information for each of the following networks:
The path starts at B and ends at X.
The path starts at H, goes through 4 other vertices, and then ends at B.
The path starts at Q, has length 3, and ends at P.
The path starts at P and ends at Q
For the following network:
State whether each of the following are valid walks:
K, F, P, K
K, P, F, K, P
K, P, F, R, M
R, P, F, M, R
K, P, F, K
F, R, M, P, F
State whether each of the following are valid paths:
K, P, F, R, M
K, P, F, K, P
K, P, F, K
A new fitness app, GetNatty, allows users to connect with each other to share their fitness goals and gains. When two people connect through the app, they are called squadmates.
The given network shows the connections six people have made in the app:
Who has the most squadmates?
Who has the least squadmates?
Are Rochelle and Clive squadmates?
The social network Bleeter allows people to share content (in the form of "Bleets") online.
Before anyone can share anything, two people must first make a connection, so one person "follows" the other. Whenever a person creates a Bleet, it is shared with everyone who follows them. These people are called "followers".
The given network represents the connections among a group of six users of Bleeter. An arrow from one vertex to another means that the first person follows the second. For example: DF follows BK.
Which user has the most followers?
Which user follows the most people?
Is this an example of a simple network? Explain your answer.
