Question 34
In a social network analysis study, researchers are examining friendship connections between users on a new platform. Initially, they observe that each user is connected to exactly k = 49 nearby users in a neighborhood-based pattern, forming a structured network with n = 100 users. However, engagement data suggest that friend recommendations introduce a small-world topology, where some connections span across distant user groups, leading to a mix of local clustering and long-range connections. To better understand this connection pattern, the researchers hypothesize that the network might instead resemble a random graph of the form G(n,p), where p is the probability of a friendship forming between any two users. Estimate the probability p that would yield the same total number of connections as in the original structured network. Report 1000p