A video-sharing platform's recommendation graph grows one video at a time
PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems
Many Parts, One Behaviour, Ch Growing networks: preferential attachment and scale-free degree distributions
Problem
A video-sharing platform's recommendation graph grows one video at a time. Each new video links to m=2 existing videos, chosen with probability proportional to their current degree, counting links made and received alike (the Barabási-Albert rule), so the attachment probability for a video of degree k is Πk=k/(2mt), with t the number of videos already present. (a) Write the rate equation for Nk(t), the expected number of videos of degree k, under this rule, stating what each term represents. (b) Using the stationary solution obtained from this rate equation with Nk=tpk, namely pk=(k−1)pk−1/(k+2) for k>m and pm=2/(m+2), compute p2 and p4.