Consider the following networks:
State the degree of vertex C.
State the degree of vertex D.
State the degree of vertex X.
State the degree of 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}
For each of the following networks:
State what the edges represent.
State what the vertices represent.
State the number of vertices.
State the number of edges.
The following network represents the internet fiber optics cables connecting several cities:
The following network represents an electrical circuit that includes a globe, resistors and multiple switches:
The following network displays newspaper routes between several houses:
The following mud map represents the roads between several towns:
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.
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.
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?
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.
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.
Rabbits and squirrels both eat plants. Foxes and hawks eat both rabbits and squirrels.
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.