State the number of vertices and the number of edges for each of the following networks:
For each of the given networks, list the pairs of vertices that have an edge between them:
State the number of loops in the following networks:
State whether the following networks contain a pair of vertices that have multiple edges between them:
An Egyptologist draws this rough map for the members of her expedition, marking out the various parts of the pyramid and how service tunnels connect these parts together.
What do the vertices of this network represent?
The company MindWork pays its three employees, Linda, Mario and Sanjay. Linda takes Mario out for lunch and gives him the money to pay for it. Mario gives his two children, Bella and Aria, some pocket money.
What do the edges of this network represent?
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:
State whether the following networks are valid or non-valid:
State whether the following are directed or undirected networks:
State whether the following statements are true or false in relation to all 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 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.
Define a simple network.
State whether the following networks are simple:
State the two changes required to make the following network simple:
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:
Is the network simple?
Is the network directed?
Who has the most squadmates?
Who has the least squadmates?
Are Rochelle and Clive squadmates?
The following network represents how a virus was transmitted among students in a class:
What do the vertices of this network represent?
Is the network directed or undirected?
Who was the first person in the class to transmit the disease to their classmates?
Who is responsible for directly infecting the most people?
Construct a directed network to represent each of the following food chain descriptions. Construct the arrows pointing from the organism that is eaten to the organism that eats it.
Rabbits and squirrels both eat plants. Foxes and hawks eat both rabbits and squirrels.
Within an aquatic biome:
Tadpoles, water beetles and snails all eat algae.
Small fish eat tadpoles, but do not like water beetles or snails.
Frogs do not eat tadpoles, and instead they eat water beetles and snails.
The kingfisher eats small fish, snails, and frogs.
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.
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.
Consider the map below which shows major roads connecting various towns. The shaded regions indicate how far each town extends:
Construct a network that represents the major roads connecting towns on the map.
Explain why this network is not directed.
Explain why this network is simple.
State the definition of a path.
Explain how a walk differs from a path.
For each of the following networks, state a valid walk that crosses each vertex once:
Determine whether the following are valid paths in the given network:
A, E, C
A, D, C
B, A, E
E, C, B
E, D, B
Determine whether the following are valid paths in the given network:
A, B, D, G, F
E, B, D, C, A
D, B, A, C, F, G
A, B, C, D, G, E
Determine whether the following are valid paths in the given network:
A, B, D, H, G, C, A
C, E, F, D, G, C
A, B, E, F, D, B, A
E, F, G, H, D, B
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:
State whether each of the following are valid paths:
