Question: Analyzing Social Connections: Exploring the Dynamics of the Dapper Network

In social networks, such as X and LinkedIn, there is the idea of a person following another person. The concept that one person follows another can be thought of as a binary relation, for example “Xenia follows Rahul”. Social networks use this “follows” relation for various purposes, for example, to show content that might be relevant to a person. This project will focus on analysing a fictious social network called “Dapper” which is described below. You will be provided with a file that represents the social network (list of users and whom they follow), based upon which you must accomplish the tasks described below.

Your tasks are to read the input and write a program that performs the following tasks.

Task 1: Give the density of the graph represented by the social network. Recall that the density of a directed graph is |E| |V |(|V |−1) , where V and E respectively represent the set of nodes and directed edges.

Task 2: Name a person who has the highest number of followers. In general, more than one person may have the same number of followers. If there is more than one person with the highest number of followers, then the name you give must be the one that is alphabetically first.

Task 3: Name a person who follows the highest number of people. Again, if there is more than one such person, again, the name you give must be the one that is alphabetically first

Task 4: A degree of separation is a measure of social distance between people. For example, people who are friends are separated by one degree. Two people who are not friends, but have a common friend are separated by two degrees. For a person P in Dapper, we define people at two degrees of separation from P as follows. • P’s followers are at one degree of separation from P. • Followers of P’s followers who are neither P nor at one degree of separation from P are at two degrees of separation from P. For the first person who appears in the input, give the number of people at two degrees of separation from that person.

Task 5: Give the median value for the number of followers in the network, that is, over the data set whose elements consist of the number of followers for each person in the network. Note that the median value is the middle element in a data set – half the data elements are smaller than the median value and half the data elements are larger. Make sure you handle the case when the number of elements is even, in which case you have no unique middle element, but two middle elements. CLARIFICATION: In such a case, you must average the two middle elements, which means that the answer may not be an integer.

Task 6: In Dapper, a message originating from a person is automatically propagated to their followers and the followers’ followers, and so on (obviously in an acyclic manner; that is, a person doesn’t get the same message more than once). Imagine you are an advertiser (you yourself are outside the social network) who wants to spread information about a new product to as many people as possible in Dapper. However, the catch is you can enrol only one person in the network to spread information on your behalf. Whom would you enrol? Again, if you determine that two or more people are equally worthy of being enrolled, you must give the name that is alphabetically first.