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:
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?
Construct a directed network to represent the following food chain description. Construct the arrows pointing from the organism that is eaten to the organism that eats it.
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.
A small area of ocean was observed over several weeks by biologists. They found that:
Killer whales depended on salmon as a primary food source. They also were observed to eat blue sharks.
The blue sharks were observed to eat squid, salmon, and crabs, while the salmon ate mackarel.
The squid ate mackarel, and the mackarel ate plankton, a microscopic marine plant.
The crabs were observed to eat the remains of all other animal species, scavenging their food once the animals had died.
Represent this information using a network.
The following network represents how a virus was transmitted among students in a class:
What do the vertices of this network represent?
Who was the first person in the class to transmit the disease to their classmates?
Who is responsible for directly infecting the most people?
The tiger salamander is cannibalistic, meaning it eats its own species. It is eaten by raccoons, and also eats crickets.
Draw this information using a network.
The diagram represents a city block. Some of the roads surrounding it are two way and some are one way only.
Draw a network that represents the allowed movement of traffic around the city block.
You are in charge of planning a parade in a small town. The mayor has highlighted the historic sites she wants the parade to pass by on this map, but she can’t find a route that passes each landmark only once.
Draw arrows on the diagram to indicate a route that:
Starts and ends at different landmarks and visits all the landmarks exactly once, except for one that is visited twice.
Starts and ends at the same landmark and visits all the landmarks exactly once, except for two that are visited twice.
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 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.
The game Scissors-Paper-Rock, is played between two people such that scissors beats paper, paper beats rock, and rock beats scissors.
Draw a network that represents what beats what item in the game.
A friend of yours wants to introduce 'Spock' as a fourth option. Can you find a way to make 'Scissors-Paper-Rock-Spock' fair, so that each wins and loses the same number of ways?
You suggest adding in a fifth option, 'Lizard'. Can you find a way to make'Scissors-Paper-Rock-Spock-Lizard' fair?
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.