Effects of higher-order interactions and homophily on information access inequality

TL;DR

This paper develops a higher-order framework to study time-sensitive information access inequality in socio-technical systems by introducing Hypergraphs with Hyperedge Homophily (H3) and a nonlinear, asymmetric SI contagion model (naSI). Using stochastic simulations on synthetic and real-world hypergraphs, the authors quantify group disparities with an optimal transport metric d_W and two fairness measures, acquisition fairness \alpha(f) and diffusion fairness \delta(f), revealing that hyperedge size-dependent homophily interacts with nonlinear contagion to shape who gains access and when. Key findings show that homophily amplifies inequality, especially under asymmetric transmission, while heterophily can produce minority advantages under symmetric contagion; the magnitude and direction depend on hyperedge size and contagion regime, with larger higher-order interactions playing a dominant role under superlinear spread. The real-world case studies (High School and Hospital) corroborate synthetic results, highlighting the practical impact of higher-order structure on information access and offering guidance for platform design and targeted interventions to mitigate inequalities in time-critical information flows. These contributions provide a dynamics-informed, higher-order perspective for evaluating and reducing informational disparities in complex, group-structured networks, with potential applications in diffusion of innovations, public health campaigns, and digital platform policies.

Abstract

The spread of information through socio-technical systems determines which individuals are the first to gain access to opportunities and insights. Yet, the pathways through which information flows can be skewed, leading to systematic differences in access across social groups. These inequalities remain poorly characterized in settings involving nonlinear social contagion and higher-order interactions that exhibit homophily. We introduce a enerative model for hypergraphs with hyperedge homophily, a hyperedge size-dependent property, and tunable degree distribution, called the $\texttt{H3}$ model, along with a model for nonlinear social contagion that incorporates asymmetric transmission between in-group and out-group nodes. Using stochastic simulations of a social contagion process on hypergraphs from the $\texttt{H3}$ model and diverse empirical datasets, we show that the interaction between social contagion dynamics and hyperedge homophily -- an effect unique to higher-order networks due to its dependence on hyperedge size -- can critically shape group-level differences in information access. By emphasizing how hyperedge homophily shapes interaction patterns, our findings underscore the need to rethink socio-technical system design through a higher-order perspective and suggest that dynamics-informed, targeted interventions at specific hyperedge sizes, embedded in a platform architecture, offer a powerful lever for reducing inequality.

Figures (33)

• Figure 1: Schematic overview of hypergraph formation with the H3 model, the social contagion dynamics of the naSI model, and inequality measurement with $d_W$.(a) Each node $v$ is assigned a group $g_v \in \{0,1\}$ (green and purple) and a hidden variable $\kappa_v$ from a group-specific distribution $\rho_{g_v}(\kappa)$, encoding its propensity to participate in hyperedges and, therefore, its degree. (b) We fix the hyperedge homophily pattern by setting the number $m_{s,r}$ of hyperedges of size $s$ and type $r$. (c) We randomly place nodes $v$ into hyperedges $e$ with probability $p(\kappa_v,g_v)$ determined by their groups $g_v$ and hidden variables $\kappa_v$. (d) An example contagion step, where node $v=1$ transmits information to either (i) node $v'=4$ or (ii) node $v'=6$ through a shared hyperedge with different rates $\beta_{g_{v'}}(e)$ depending on the group membership of $v'$. Dotted red borders indicate informed nodes. Even though all nodes are informed, (e) shows that, when nodes are ranked by the time they are informed, differences emerge in group-wise rank distributions $\mathcal{Z}_g$, which we compare using the Wasserstein distance $d_W$.
• Figure 2: Quantifying information access inequality in random hypergraphs. By simulating different contagion processes on hypergraphs randomly sampled from our model, we measure the effect of hyperedge homophily patterns on information access inequality. Top row: distribution of Wasserstein distances $d_W(\mathcal{Z}_0, \mathcal{Z}_1)$ between group-wise empirical rank distributions under (a) linear, (b) sublinear, (c) superlinear, and (d) asymmetric transmission. Middle row: violin plot distributions of time $t^{(g)}_{90}$ required to inform $90$% of the majority $g=0$ (darker shade, left side of violin) or minority $g=1$ (lighter shade, right side of violin) under (e) linear, (f) sublinear, (g) superlinear, and (h) asymmetric transmission. Bottom row: average fraction of transmission events involving hyperedges of size $s$, stratified by group, under (i) linear, (j) sublinear, (k) superlinear, and (l) asymmetric transmission. Darker bars indicate transmission among majority nodes; lighter bars indicate transmission among minority nodes. In each subplot, results from homophilous, neutral, and heterophilous hypergraphs are shown in shades of blue, gray, and orange, respectively. All results are averaged over $n_\mathrm{hg}=10^3$ independent simulations of the naSI model on hypergraphs generated from the H3 model with the same structural characteristics. Inequality in information access emerges across hyperedge homophily patterns and social contagion types, with interactions between structure and dynamics driving stark group-level differences, particularly under asymmetric and superlinear processes.
• Figure 3: Measuring group-level differences in acquiring and spreading information. We assess information access inequality using two fairness measures applied to simulated contagion processes on hypergraphs with varying hyperedge homophily patterns. Top row: acquisition fairness, $\alpha(f)$, which captures a group's ability to receive information, under (a) linear, (b) sublinear, (c) superlinear, and (d) asymmetric contagion dynamics. Bottom row: diffusion fairness, $\delta(f)$, which captures a group's ability to spread information, under (e) linear, (f) sublinear, (g) superlinear, and (h) asymmetric contagion dynamics. Results are averaged over $n_\mathrm{hg}=10^3$ simulations of the naSI model on homophilous (blue), heterophilous (orange), and neutral (gray) hypergraphs generated from the H3 model. The dashed black line indicates equality, while $\alpha(f),\delta(f)>1$ denote a minority advantage and $\alpha(f),\delta(f)<1$ indicate a majority advantage. We estimate $99$% confidence intervals using $100$ bootstrap samples. The minority group is disadvantaged in both access and spread under homophilous conditions and under asymmetric transmission, but gains an advantage under symmetric, heterophilous dynamics.
• Figure 4: Quantifying information access inequality on hypergraphs with mixed hyperedge homophily patterns. We simulate four contagion processes on synthetic hypergraphs that combine neutral connectivity with either homophilous or heterophilous interactions at specific hyperedge sizes, and assess group-level differences in time-critical information access. Rows $1$ and $3$: distributions of Wasserstein distances $d_W(\mathcal{Z}_0,\mathcal{Z}_1)$ between majority and minority rank distributions. We display results for mixed homophilous-neutral hypergraphs under (a) linear, (b) sublinear, (c) superlinear, and (d) asymmetric contagion and results for heterophilous-neutral hypergraphs under (i) linear, (j) sublinear, (k) superlinear, and (l) asymmetric contagion. Rows $2$ and $4$: violin plots of $t^{(g)}_{90}$, the time to reach $90$% of nodes in the majority $g=0$ (darker, left violin) and minority $g=1$ (lighter, right violin) groups. We display results for mixed homophilous-neutral hypergraphs under (e) linear, (f) sublinear, (g) superlinear, and (h) asymmetric contagion and results for heterophilous-neutral hypergraphs under (m) linear, (n) sublinear, (o) superlinear, and (p) asymmetric contagion. Mixed homophilous patterns are shown in shades of blue, while mixed heterophilous patterns are shown in orange. All results are averaged over $n_\mathrm{hg}=10^3$ independent simulations of the naSI model on hypergraphs generated from the H3 model with the same structural characteristics. Inequality is amplified when homophilous or heterophilous patterns are localized in hyperedges that reinforces the dominant social contagion pathway, meaning that hyperedge-level structure, as well as dynamical factors jointly shape information access.
• Figure 5: Homophily patterns and information diffusion inequality in the High School hypergraph.(a)-(d) Hyperedge homophily $h_{s,r}^{(g)}$ is shown for hyperedge sizes $s\in\{2,3,4,5\}$ for majority ($g=0$, green) and minority ($g=1$, purple) groups. The dashed line shows the expected value under random mixing; values above indicate over-representation. Inequality is captured by (e) distributions of Wasserstein distances $d_W(\mathcal{Z}_0,\mathcal{Z}_1)$, (f) violin plots of the time $t^{(g)}_{90}$ to inform 90% of majority (left) and minority (right) nodes, (g) acquisition fairness $\alpha(f)$, and (h) diffusion fairness $\delta(f)$. Panels (e)–(h) average results over $n_\mathrm{hg}=10^3$ simulations for linear (blue), sublinear (pink), superlinear (red), and asymmetric (green) contagion. Confidence intervals in (g),(h) are estimated from $100$ bootstrap samples. The unique homophily pattern yields a majority advantage under asymmetric contagion, but a minority advantage under sublinear contagion.