How Predicted Links Influence Network Evolution: Disentangling Choice and Algorithmic Feedback in Dynamic Graphs

TL;DR

A temporal framework based on multivariate Hawkes processes is proposed that disentangles intrinsic interaction tendencies with amplification effects induced by network dynamics and algorithmic feedback and introduces an instantaneous bias measure derived from interaction intensities, capturing current reinforcement dynamics beyond cumulative metrics.

Abstract

Link prediction models are increasingly used to recommend interactions in evolving networks, yet their impact on network structure is typically assessed from static snapshots. In particular, observed homophily conflates intrinsic interaction tendencies with amplification effects induced by network dynamics and algorithmic feedback. We propose a temporal framework based on multivariate Hawkes processes that disentangles these two sources and introduce an instantaneous bias measure derived from interaction intensities, capturing current reinforcement dynamics beyond cumulative metrics. We provide a theoretical characterization of the stability and convergence of the induced dynamics, and experiments show that the proposed measure reliably reflects algorithmic feedback effects across different link prediction strategies.

Figures (7)

• Figure 1: Empirical vs. instantaneous bias from two simulated Hawkes processes across three phases: initial moderate activity ($t<500$), intermediate polarization ($500 \leq t < 1000$), and final alignment of group excitation ($t \geq 1000$).
• Figure 2: Results on synthetic data. Left: Mean self-excitation coefficients $\alpha_{(i,j)}$ estimated for each model, where entry $(i,j)$ represents the estimated self-excitation of the interaction process between groups $i$ and $j$. Right-top: $B_{emp}(t)$ evolution: full timeline v.s. post-intervention phase. Right-bottom:$B^*_{inst}(t)$ evolution: full timeline v.s. only LP-intervention phase.
• Figure 3: $B^*_{\mathrm{inst}}$ around the German federal election of 2021.
• Figure 4: Network evolution and equilibrium intensities under two algorithmic scenarios on a two-group professional network (men M, women F). Left: snapshots of the interaction network at three time points, with edge width proportional to the mean-field intensity $\bar{\lambda}_{ij}(t)$. Under the standard scenario (top row, $E_{12} = 0.05$), within-group interactions (blue: M--M, red: F--F) progressively dominate, reflecting the amplification of baseline homophily through self-excitation. Under the fairness-aware scenario (bottom row, $E_{12} = 0.90$), cross-group interactions (green: M--F) are reinforced instead. Right: (a) stationary mean intensities $\bar{\lambda}^*$ at equilibrium; (b) mean-field convergence trajectories $\bar{\lambda}_{ij}(t)$. The fairness-aware intervention reduces $\bar{\lambda}^*_{11}$ and increases $\bar{\lambda}^*_{12}$ relative to the standard scenario
• Figure 5: Empirical verification of Proposition \ref{['prop:convergence']}. The normalized distance $\|\bar{\boldsymbol{\lambda}}(t) - \bar{\boldsymbol{\lambda}}^{*(k)}\| / \|\bar{\boldsymbol{\lambda}}(\tau_k) - \bar{\boldsymbol{\lambda}}^{*(k)}\|$ (solid line) remains below the exponential bound $e^{-\kappa_k(t - \tau_k)}$ (dashed line) on each interval $[\tau_k, \tau_{k+1})$, with $\kappa_k = 0.9\,\beta(1 - \rho(\mathbf{A}^{(k)}/\beta))$. The excitation matrix $\mathbf{A}^{(k)}$ changes twice, inducing a new local equilibrium $\bar{\boldsymbol{\lambda}}^{*(k)}$ and a fresh convergence phase at each transition.

Theorems & Definitions (8)

• Definition 3.1: Group-Pair Hawkes Intensity Model
• Definition 3.2: Empirical bias measure
• Definition 3.3: Instantaneous bias
• Proposition 1: Group-level mean-field dynamics
• Proposition 2: Exponential convergence rate
• Proposition 3: Exponential convergence rate - locally stationary case
• proof
• proof