Disassortative mixing in decentralized social network due to reciprocal links

Social networks are known to exhibit assortative mixing, and specifically positive degree–degree coefficients, due to homophily of nodes with similar degrees. However, we found that in the decentralized social network Farcaster, assortative coefficients are negative throughout the growth period we examined, even though it shares some similar patterns to centralized social networks, including heavy-tailed degree distribution and preferential attachment. By studying the detailed growth mechanism of this network, we found that when a user follows someone (followee), there is a significant probability the followee will follow back the user, i.e. reciprocal follow-back. We further construct a novel mechanistic network growth model calibrated from empirical data. Through simulations and sensitivity analysis on the model parameters, we confirm that the disassortative mixing is due to the reciprocal follow-back mechanism. Through percolation analysis, we also demonstrate that the disassortative network from such mechanism has a much lower percolation transition threshold, indicating that information is much more likely to become viral compared to the one without reciprocal follow-backs.