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Assignment

You are tasked with analysing various datasets representing different types of social and communication behaviour. These datasets are provided as files and can be found alongside this coursework pro-forma on Learning Central. You should ONLY use the files provided as they are intentionally modified versions of public datasets.

Alongside the dataset files, there are 3 (THREE) IPython notebooks, named part-1.ipynb, part-2.ipynb, and part-3.ipynb, which you should solely use to complete the assignment and submit these in line with the Submission Instructions section above. The cells in each completed notebook will be ran in the order that they appear. You do not need to resubmit the dataset files.

You are required to address 16 total questions across the 3 parts. Each part is made up of 1 or 2 tasks containing multiple questions. These questions are also listed below for convenience.

For EACH question in EACH notebook:

1. Complete the cell below each question marked with “#CODE:” with the Python

code needed to generate any new information you need for your answer. This information should be outputted when the cell is ran and any floating-point values should be presented to 2 decimal places unless they are less than 0.01.

2. Complete the cell below this marked with “ANSWER:” with your answer to the

question, referring to the information outputted above (as well as any previous cell if needed). In doing so, briefly explain your approach and methods/measures used to answer the question and justify any choices made. Each answer cell should (ideally) be no more than 125 words.

Each question is worth 6 marks (making a total of 96/100 possible marks) and a further 4 marks (4/100) will awarded for the overall usability and readability of the notebooks submitted. Marks will be awarded using the criteria described in the Criteria for assessment section below.

You may use any Python packages installable via pip.

“%pip install ” commands should be placed in the cell below “Install Python packages (pip only)” provided at the top of each notebook.

“import ” lines for all packages required for the notebook to be ran successfully should be placed in the cell under “Import Python packages” provided at the top of each notebook.

You may add additional cells throughout the notebooks, but this should be minimised.

Questions (duplicated from the three notebook files)

Part 1: Social media behaviour data

Task 1 of 1

Examine the Graph Modelling Language (gml) files "socialmedia_cmt224_reply_network.gml" (reply network) and "socialmedia_cmt224_social_network.gml" (social network) which represent Twitter data between a sample of users over several days at the time of the Higgs boson particle discovery. Both networks are directed and share the same ids for nodes (anonymised Twitter users). However, the shared user ids are contained within the "label" attribute in the .gml files, not the node "id" attribute of each individual .gml file.

In the reply network, an edge from a node, u, to some other node, v, indicates that u replied to a Tweet made by v during the time period. Replies are also Tweets. Edges are weighted with the weight representing the number of times this happened over the time period.

In the social network, an edge from node u to v indicates that u follows v on the social media platform.

Using these networks, answer the following questions:

Q1. What fraction of users do not reply to or follow any other user, but have had others reply to their Tweets?

Q2. How does the topological structure of the reply network differ from the social network

in terms of overall sparsity of edges between users and the number of connected groups of users?

Q3. Does the number of users a user follows in the social network correlate with the number of replies that they make?

Q4. Is a user that replies to another user's Tweet multiple times more likely to follow that user in comparison to if they only replied once?

Q5. How many users have only mutual following connections (i.e., every user they follow also follows them) and only mutual reply connections with these same users?

Part 2: Email behaviour data

Task 1 of 2

Examine the file "emails_cmt224.edgelist" which represents email behaviour at an organisation. Each line contains two numbers, u and v, separated by a blank space. Consider each number as an identifier for an individual in the organisation, with the space on each line representing that the individual, u, sent at least one email to the other individual, v, at some point. Model the data using an appropriate, directed network representation and answer the following questions:

Q1. Do the majority of individuals have a higher or lower ratio of mutual connections than average in the network?

Q2. Using the largest, strongly connected component (where at least one path exists

between each individual and all others). Could the connectivity of the component be suggested to be reflective of a small world phenomenon in comparison to the typical connectivity of 10 comparative random networks?

Q3. Are occurrences of induced, connected subgraphs of 3 individuals (triads) with only

mutual connections more abundant in the largest, strongly connected component than those with a mixture of asymmetric and mutual connections? What does this suggest about how mutual connections are distributed in the component?

Task 2 of 2

Examine the JSON file "emails_cmt224_departments.json" (departments file). Keys in the departments file represent individuals using the same ids as in the "emails_cmt224.edgelist" file in Part 2, Task 1 and the values represent a department id that the individual can be attributed to. Using the contents of the departments file in combination with the network in Part 2, Task 1, answer the following questions:

Q1. Using the connections that individuals have in the network, are they more likely to

mix with others in their department or those with a similar number of outward connections?

Q2. Are all departments with 15 or more members more tightly connected amongst

themselves in comparison to all individuals across the overall network irrespective of their department? Where in this context, 'more tightly connected' is defined as having more mutual AND clustered connections. In addition to answering the overall question as yes or no, provide a list of departments this is true for (if any) and not true for (if any).

Part 3: Peer-to-peer message behaviour data

Task 1 of 2

Examine the file "p2p_msg_cmt224.csv" which represents messaging behaviour between users on a messaging platform. Each row has four columns, representing a single event where a person (person_a) messaged another person (person_b) on some date (date) at some time of day (time). From this, answer the following questions:

Q1. Build a suitable network to represent social connections based on the messaging

behaviour that took place in the first 28 days. In doing so, assume that one or more messages from one person to another represents a mutual underlying social connection (i.e., regardless of whether person_a messaged person_b, person_b messaged person_a, or both at some point).

Q2. Using the largest connected component of the network constructed in Task 1, Q1.

What is the mean, median and the standard deviation of the differences between the maximum degree of separation of each individual and the average distance between the individual and all others?

Q3. Build another suitable network to represent social connections based on ALL

message behaviour in the dataset. In doing so, assume that one or messages from one person to another represents a MUTUAL underlying social connection (i.e., regardless of whether person_a messaged person_b, person_b messaged person_a, or both at some point). Can the social phenomenon, ‘Triadic Closure’, be supported for the common nodes that exist in both the network created from behaviour for the first 28 days (i.e., from Task 1, Q1) and the network built from all message behaviour?

Q4. What hypothetical, non-existent edges would need to be added to the network

representing all message behaviour (i.e., from Task 1, Q3) such that a message could pass along a path from any node to any other? In doing so, aim to minimise the number of edges that would be needed as well as the longest shortest path in the network as a result.

Task 2 of 2

Using the largest connected component of the social network constructed from all data in Task 1, Q3, assume the role of an outsider with complete visibility of the network that now wishes to spread a hypothetical message such that everyone in the component would know the information it contained as quickly as possible. Assume that messages will now spread in sequential timesteps using the following mechanism. If an individual is told the message at timestep :, the individual will forward the message to all of their direct connections at timestep :+1. Individuals can therefore be told the message more than once. From this, answer the following questions:

Q1. If you could only select 1 individual to tell at timestep 0, what set of nodes could

you select from which would result in the message being received by everyone in the fewest timesteps as possible and what would the number of timesteps be?

Q2. If you had to select any 5 individuals to tell at timestep 0, can the message be

received by everyone in fewer timesteps than the single individual selection in Q1? In determining your answer, use one or more appropriate network connectivity measures, rather than an exhaustive search through every combination of nodes in the network.

Learning Outcomes Assessed

1. Analyse fundamental traits of complex networks by synthesising theoretical concepts and methodologies from graph theory.

2. Evaluate and implement computational approaches to model and visualise complex social phenomena.

3. Design and create software to investigate or support human interaction behaviour.

Criteria for assessment

Credit will be awarded against the following criteria. There are 100 marks available for this assignment. Each of the 16 questions are worth 6 marks, split between up to 3 marks for the approach and implementation and up to 3 marks for the explanations and justifications of the approach and implementation. This totals 96/100 possible marks. Marks will be awarded using the following criteria:

0 marks	1 mark	2 marks	3 marks
Unsuitable	Partially completed	Completed	Complete
implementation that	implementation that	implementation with	implementation with
does not address the	uses some appropriate	mostly appropriate	appropriate selection
question.	selection of appropriate methods and measures.	selection and implementation of	and implementation of methods and measures.
OR		appropriate methods and measures.
Non completion of the question.
0 marks	1 mark	2 marks	3 marks
Little to no explanation	Partially incorrect	Some explanation of	A clear, concise
of the approach taken	description/explanation	approach taken in the	explanation and
in the implementation.	of the approach taken	implementation with	justification of the
Or the explanation is	in the implementation.	an explanation of why	approach taken,
incorrect.		the specific methods	including comparison
	OR	or measures were	against alternative, and
OR		selected in the	potentially worse,
	A brief description of	implementation, but	choices of the methods
Non completion of the	the overall approach	little to no	or measures used
question.	used in the implementation, but with missing or limited explanations of the why the specific methods or measures were used.	explanation for why they are the most appropriate choice.	where relevant.