State the degree of the following vertices:
Vertex C
Vertex D
Vertex X
Vertex C
For each of the following networks:
Create an adjacency matrix for the network.
State the degree of each of the vertex.
Create an adjacency matrix for each of the following networks:
Construct a network for each of the following matrices:
\begin{matrix} & \begin{matrix} X & Y & Z \end{matrix} \\ \begin{matrix} X \\ Y \\ Z \end{matrix} & \begin{bmatrix} 0 \, & \, 0 & \, 0 \\ 2 \, & \, 0 & \, 0 \\ 1 \, & \, 1 & \, 0 \end{bmatrix} \end{matrix}
\begin{bmatrix} 0 & 0 & 1 & 1 & 1 \\ 0 & 0 & 2 & 0 & 0 \\ 1 & 2 & 0 & 0 & 0 \\ 1 & 0 & 0 & 2 & 0 \\ 1 & 0 & 0 & 0 & 2 \end{bmatrix}
\begin{matrix} & \begin{matrix} A & B & C & D \end{matrix} \\ \begin{matrix} A \\ B \\ C \\ D \end{matrix} & \begin{bmatrix} 0 \, & \, 0 & \, 1 & \, 1 \\ 0 \, & \, 0 & \, 1 & \, 1 \\ 1 \, & \, 1 & \, 0 & \, 1 \\ 1 \, & \, 1 & \, 1 & \, 0 \end{bmatrix} \end{matrix}
\begin{matrix} & \begin{matrix} A & B & C & D \end{matrix} \\ \begin{matrix} A \\ B \\ C \\ D \end{matrix} & \begin{bmatrix} 0 \, & \, 1 \, & \, 0 & \, 0 \\ 1 & \,1 & \,0 & \,1 \\ 0 & \,0 & \,1 & \,1 \\ 0 & \,1 & \,1 & \,0 \end{bmatrix} \end{matrix}
\begin{matrix} & \begin{matrix} P & Q & R & S & T\end{matrix} \\ \begin{matrix} P \\ Q \\ R \\ S \\ T \end{matrix} & \begin{bmatrix} 0 \, & \, 1 & \, 2 & \, 0 & \, 0 \\ 1 & \,0 & \,0 & \,0 & \,0 \\ 2 & \,0 & \,0 & \,1 & \,0 \\ 0 & \,0 & \,1 & \,1 & \,1 \\ 0 & \,0 & \,0 & \,1 & \,0 \end{bmatrix} \end{matrix}
\begin{matrix} & \begin{matrix} A & B & C & D & E \end{matrix} \\ \begin{matrix} A \\ B \\ C \\ D \\ E \end{matrix} & \begin{bmatrix} 0 \, & \, 2 & \, 0 & \, 0 & \, 0 \\ 0 & \,0 & \,0 & \,1 & \,0 \\ 1 & \,0 & \,0 & \,0 & \,1 \\ 0 & \,0 & \,1 & \,0 & \,0 \\ 0 & \,0 & \,0 & \,2 & \,0 \end{bmatrix} \end{matrix}
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. So DF follows BK.
What kind of network, directed or undirected, represents the connections people form on Bleeter?
Which user has the most followers?
Which user follows the most people?
Is this an example of a simple network? Explain your answer.
Construct a directed graph to represent each of the following food chain descriptions. Construct the arrows pointing from the animal that is eaten to the animal that eats it.
Within a water system:
Tadpoles, water beetles and snails all survive by eating algae.
Small fish eat the tadpoles, whilst frogs survive on water beetles and snails.
The kingfisher, a skillful fishing bird, survives on eating small fish and frogs.
Rabbits and squirrels both eat plants. Foxes and hawks eat both rabbits and squirrels.
The killer whale depends on tuna as a primary food source. In turn, the tuna feeds on fish called mackerel. For mackerel to survive, they depend on microscopic organisms collectively known as zooplankton.
Consider the map below which shows major roads connecting various towns. The shaded regions indicate how far each town extends:
Construct a graph that represents the major roads connecting towns on the map.
A beach volleyball team of 5 players can use 3 players in any one game.
The table shows the combinations that the coach has already used in the first three games:
| Games | Players chosen |
|---|---|
| 1 | Ryan, Jimmy, Lucy |
| 2 | Lucy, Beth, Ellie |
| 3 | Ellie, Ryan, Jimmy |
Construct a network to represent this information.
There is one more game left in the tournament. Which players should the coach choose so that every team member has played with every other team member at least once?
A group of journalists have been asked to work in pairs to collaborate on an article.
Derek has already collaborated with Neil, Xavier, and Xanthe.
Neil has already collaborated with Xanthe, Xavier, and Tina.
Xanthe and Tina have collaborated together.
Construct an undirected graph to represent the journalists who have worked together.
Name the journalists who still need to collaborate with someone else so that each journalist will have collaborated with every other journalist at least once.
Over a year students work in pairs to complete poster projects.
A group of 4 friends have already completed the following projects together:
| Project | Pair who worked on it |
|---|---|
| Electricity | Aaron and Rochelle |
| Solar Energy | Aaron and Bianca |
| Water Cycle | Mario and Rochelle |
| Acid Rain | Mario and Bianca |
Construct an undirected graph to represent the pairs of students who have completed projects together.
Name the pairs of students that should work together on the next poster project so that all 4 friends have worked with each other.
Consider the following image which shows a train network, and the stations that are connected by train lines:
Construct the graph that represents the train network.
The following table displays the times buses arrive and depart from several bus stops:
| Teribithia | 1 : 39 am | 4 : 23 am | |
|---|---|---|---|
| Narnia | 6 : 36 am | 8 : 44 am | |
| Nod | 4 : 29 am | 9 : 29 am | |
| Oz | 5 : 36 am | 8 : 18 am | 11 : 51 am |
Construct the graph that represents the bus routes.