Create your graph. Each student will receive a unique weighted, undirected graph based on their

ID number. To create your graph, go to the Canvas assignment page for the Investigative Report

and enter your details $($student ID and last name$).$ The graph will appear for you to download. If

you lose your graph, you can return and retrieve it by entering your details again.

Decide on a context. Graphs come from multiple real$-$life situations. Some were discussed in the

lectures and tutorials. You are to think of one that is appropriate for your graph. This will be used

in the introduction to your report. Here are some examples you may like to use $($although you

may not copy and paste my wording$),$ or you can use one your own:

$$ A company has hired you to analyse their company website. The vertices represent the

pages on the website, the edges represent which pages link to each other $($assume that

no page links to another page without it linking back$),$ and the weights represent how far

down the page the link is $(1=$top, $6=$bottom$)$;

$$ Analyse the graph. Investigate the graph. Think of what we discussed in lectures and tutorials.

Calculate important quantities, see if you can find different characteristics and components of

the graph. Your investigation should include:

o The number of vertices and edges;

o The degrees of the vertices;

o Whether it is connected;

o The edge$-$endpoint function;

o The presence or absence of types of walks $($trails$/$paths$/$circuits$,$ Euler, Hamiltonian$)$;

o The minimal spanning tree and what algorithm you used to find it; and

o Anything else that you find of interest.

$$ Write the report. Do NOT just list what you found. You are to write a report that has a structure

to it$.$ It should not be hand$-$written. It should have:

o A title. Give the report a title based on your context.

o An introduction. Introduce the problem you decided on and the graph that you have

$($include the image with a caption and reference it in$-$text$).$ Explain why you are analysing

it $($why would it be useful to know these things$).$

o A body. Discuss your analysis. What did you find? Would this have any specific meaning

for your problem? Write in full sentences and paragraphs. Include any images that would

illustrate your points or are important graphs.

o A conclusion. Briefly summarise your report and relate it back to your context.

o Images. You are analysing something visual, include any images$/$graphs that are

appropriate $($these could be annotated to show features of the graph$).$ Ensure they all

have captions describing what they are $($if I take it out of the report, then is it still

understandable what is being shown?$)$ and are all referenced in text by the number.