How Recommendation Algorithms Shape Social Networks: An Adaptive Voter Model Approach

TL;DR

This work analyzes how social media-like link formation via local versus global rewiring affects polarization and echo chambers using an adaptive voter model. By simulating AVMs on ER, WS, and BA networks, it shows that neighbor-based, local rewiring amplifies fragmentation into many small, like-minded components and elevates polarization, especially in clustered, homophilic settings. The findings imply that platform algorithms can mechanically intensify echo chambers by reshaping network structure, with tangible changes to degree distributions and convergence dynamics. Overall, the study provides a mechanistic link between algorithmic design and social fragmentation, offering directions for empirical calibration and future model extensions.

Abstract

The rise of social media and recommendation algorithms has sparked concerns about their role in fostering opinion polarization and echo chambers. We study these phenomena using an adaptive voter model to compare two connection mechanisms: "free" global rewiring, where individuals connect with anyone sharing their opinion, and "friend-of-a-friend" local rewiring, which mimics algorithmic link recommendations on platforms like Facebook or LinkedIn. Simulations across different network topologies reveal that local rewiring increases final-state polarization of the system and fragments social networks into many disconnected components. The usual phase transition into two disconnected components turns into a fragmentation of smaller components, leading to an increase in echo chambers as well as many isolated nodes. This effect is most pronounced in clustered networks with high homophily in rewiring, illustrating how recommendation algorithms can intensify social fragmentation by changing the very structure of the network.

Figures (11)

• Figure 1: Examples of the different rewiring and opinion update dynamics in a minimal setup. Each color represents a different opinion (for example red = 1, blue = 0). Global rewiring here leads to two equally likely outcomes if the bottom right node is selected, for the other two processes only one update choice exists.
• Figure 2: Homophily measure $H$ with individual homophily measures $h_{1-4}$ magnetization $|M|$ and the number of echo chambers $EC$ for three simple graphs with arbitrary opinion assignment (for example, red = 1 and blue = 0). Consensus within the graph or disconnected subgraphs both corresponds to maximal homophily with $H = 1$, as all neighbors share the same opinion in both cases. Magnetization allows us to distinguish between those cases.
• Figure 3: Overview of the two homophilic rewirings for a WS network with $N = 100$. The initial graph (top middle) fragments into multiple smaller components (top left and top right) for local rewiring $p_{l}>0$, compared to two main components (bottom left and bottom right) for global rewiring $p_{g}$. Imitation only (bottom middle) leads to consensus.
• Figure 4: Overall homophily $H$, absolute value of the overall magnetization $|M|$ and the number of echo chambers (shifted by one) $EC+1$ over time $t$ for an ER (top four) and a WS network (bottom four) with $N = 100$ and average degree $k_{avg} = 4$ for different rewiring probabilities. The measures of the BA network (not shown) are essentially the same for the ER network.
• Figure 5: Echo chamber distribution $P(s_i)$ of disconnected subgraphs $s_i$ for an ER (top row), a WS (middle row) and a BA network (bottom row) with $N = 100$ and $k_{avg} = 4$, excluding isolated nodes. In case of no rewiring $p_g = p_l = 0$ only one big cluster exists, indicated by the datapoint in the top right corner in each subfigure.