Meritocracy versus Matthew-effect: Two underlying network formation mechanisms of online social platforms

TL;DR

This work proposes two fundamental network formation mechanisms: a meritocracy-based model and a Matthew-effect-based model, designed to capture the formation logic underlying traditional and emerging social networks, respectively, and demonstrates that both models replicate salient statistical features of social networks including scale-free and small-world property.

Abstract

With the rapid development of the internet industry, online social networks have come to play an increasingly significant role in everyday life. In recent years, content-based emerging platforms such as TikTok, Instagram, and Bilibili have diverged fundamentally in their underlying logic from traditional connection-based social platforms like Facebook and LinkedIn. Empirical data on follower counts and follower-count-based rankings reveal that the distribution of social power varies significantly across different types of platforms, with content-based platforms exhibiting notably greater inequality. Here we propose two fundamental network formation mechanisms: a meritocracy-based model and a Matthew-effect-based model, designed to capture the formation logic underlying traditional and emerging social networks, respectively. Through theoretical and numerical analysis, we demonstrate that both models replicate salient statistical features of social networks including scale-free and small-world property, while also closely match empirical patterns on the relationship between in-degrees and in-degree rankings, thereby capturing the distinctive distributions of social power in respective platforms. Moreover, networks such as academic collaboration networks, where the distribution of social power usually lies between that of traditional and emerging platorms, can be interpreted through a hybrid of the two proposed mechanisms. Deconstructing the formation mechanisms of online social networks offers valuable insights into the evolution of the content ecosystems and the behavioral patterns of content creators on online social platforms.

Figures (4)

• Figure 1: | Data analysis of real-world online social platforms.A Relationship between users' follower counts and their follower-count-based ranking on connection-based networks (e.g., Facebook Indiana university), content-based networks (e.g. Bilibili Science & Education category), and mixed-mechanism networks (e.g. ArXiv Condensed Matter collaboration network) under log-log coordinates. Network link density is normalized for comparability, and consistent results have been observed across different categories and communities of various online platforms. B Gini coefficients of follower counts across different types of platforms: Facebook (Indiana, Georgetown, Berkeley, Michigan), Arxiv collaboration networks (Condensed Matter, Astro Physics, High Energy Physics), and Bilibili (Science & Education, Food Reviews, Daily Life, Anime Commentary).
• Figure 2: | Network formation mechanism of the proposed models. Illustration of network formation mechanism in A Matthew-effect-based model and B meritocracy-based model, where the former is primarily influenced by in-degree $d_j^{\text{in}}$, while the latter is determined by content quality $q_j$. C Empirical evidence of the limited-attention assumption on Twitch: variation in the proportion of followed streamers in the poker and art categories with respect to user account age.
• Figure 3: | Verification of scale-free and small-world property.A,B Power-law in-degree distribution verification of the meritocracy-based model (A) and the Matthew-effect-based model (B), using a network size of $N = 10,000$. C,D Network diameter and average path length calculation of the meritocracy-based model (C) and the Matthew-effect-based model (D), together with a $\log_2(N)$ benchmark curve. E Average clustering coefficient calculation of the meritocracy-based model ($p=1$), the Matthew-effect-based model ($p=0$) and a hybrid model combining the two mechanisms with equal probability ($p=0.5$). The average clustering coefficient of a directed Erdős–Rényi model with same network density is provided as a reference. F Average clustering coefficient under different mixing ratio $p$. Simulation experiments were conducted with $100$ runs for each model under an in-degree constraint of $M = 5$. All the results remain consistent for different values of $N$ and $M$ (See Supplementary).
• Figure 4: | Variations in social power distribution across online social networks.A-C Comparison of social power distributions in (A) content-based platforms vs. connection-based platforms based on real-world data, and (B,C) the meritocracy-based model vs. the Matthew-effect-based model, based on simulation results and analytical approximation results of the proposed theoretical models. D,E Visualization of in-degrees for the top 5,000 nodes in the meritocracy-based model and Matthew-effect-based model. F Social power distributions resulting from different proportions of the two network formation mechanisms, with $p = 0$ indicating a fully Matthew-effect-based process and $p = 1$ indicating a fully meritocracy-based process. G Variation in the Gini coefficient with respect to the mixing proportion $p$ between the two network formation mechanisms. All conclusions based on the theoretical models are illustrated under a network size of $N=10000$ and an out-degree constraint of $M=5$, with similar patterns observed across different values of $M$.