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

Mathilde Perez; Raphaël Romero; Jefrey Lijffijt; Charlotte Laclau

cs.SIMar 4, 2026

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

Authors: Mathilde Perez, Raphaël Romero, Jefrey Lijffijt, Charlotte Laclau

Organizations: LTCI, Télécom Paris, Institut Polytechnique de Paris, France. · IDLab , Ghent University , Belgium.

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 & tables

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

Panel of Figure 2 — 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.

	Without retrain				With retrain
Model	AUC	AUC 1	$B^{*}_{inst}$	$\Delta DP$	$B^{*}_{inst}$	$\Delta DP$
GCN	$0.84_{\pm 0.01}$	$0.97_{\pm 0.00}$	$0.75_{\pm 0.02}$	$0.37_{\pm 0.04}$	$0.80_{\pm 0.03}$	$0.43_{\pm 0.03}$
Crosswalk	$0.84_{\pm 0.01}$	$0.96_{\pm 0.01}$	$0.73_{\pm 0.01}$	$0.35_{\pm 0.02}$	$0.81_{\pm 0.02}$	$0.43_{\pm 0.04}$
DeBayes	$0.85_{\pm 0.01}$	$0.88_{\pm 0.00}$	$0.64_{\pm 0.01}$	$0.18_{\pm 0.02}$	$0.63_{\pm 0.02}$	$0.18_{\pm 0.01}$
UGE	$0.86_{\pm 0.01}$	$0.88_{\pm 0.01}$	$0.68_{\pm 0.01}$	$0.24_{\pm 0.03}$	$0.71_{\pm 0.02}$	$0.31_{\pm 0.03}$
Node2Vec	$0.85_{\pm 0.01}$	$0.94_{\pm 0.01}$	$0.63_{\pm 0.02}$	$0.20_{\pm 0.02}$	$0.65_{\pm 0.02}$	$0.20_{\pm 0.02}$

Table 1: AUC, homophily

B^{*}_{inst}

and

\Delta DP

averaged over 10 runs (mean

\pm_{\text{std}}

). Without retrain : fixed embedding. With retrain : embedding recomputed in middle timeline.

Figure 3:

B^{*}_{\mathrm{inst}}

around the German federal election of 2021.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Kernel	Value	Interpretation
$\alpha_{(1,1),(1,1)}$	$0.60$	M–M self-excitation: each M–M interaction reinforces future ones
$\alpha_{(2,2),(2,2)}$	$0.40$	F–F self-excitation: weaker than M–M due to smaller group activity
$\alpha_{(1,2),(1,2)}$	$0.20$	Cross-gender self-excitation: weak without algorithmic boost
$\alpha_{(1,2),(1,1)}$	$0.10$	Cross-gender interactions mildly stimulate M–M activity
$\alpha_{(1,2),(2,2)}$	$0.10$	Cross-gender interactions mildly stimulate F–F activity
$\alpha_{(1,1),(1,2)}$	$0.05$	M–M interactions weakly stimulate cross-gender ones

Appendix

Table 2: Non-zero entries of the excitation matrix

\mathbf{A}

, i.e., excitation strengths

\alpha_{(i,j),(k,l)}

in the two-group example, with

\alpha_{0}=0.3

and

\gamma_{\mathrm{rec}}=0.5

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

Group	True $\alpha$ values			Estimated values by window
	Regime 1	Regime 2	Regime 3	Window 1	Window 2	Window 3
w	0.40	0.75	0.50	0.435	0.733	0.543
c	0.20	0.15	0.50	0.240	0.198	0.490

Appendix

Table 3: Self-excitation coefficients

\alpha

and baseline intensities

\mu

for each regime and their estimates.

Figure 5: Empirical verification of Proposition 2 . 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.

Concept	Parameter	Description
Network size	$N=300$	Total number of nodes
Sensitive groups	groups	Node group assignments
Group link probability	prob_matrix	Matrix of link formation probabilities between group pairs
Node activity	activity_rate	Probability a node is active at each time step
Popularity influence	popularity	Initial popularity score of each node in link formation
Retrain policy	$L$	Frequency of link prediction updates (periodic or single)

Appendix

Table 4: Hyperparameters used in the simulation.

Panel of Figure 6 — Figure 6: Estimated Hawkes parameters: (a) $\mu$ estimated; (b) Estimated excitation matrices $\alpha$ over two windows [300–450] and [450–600].

Camp	Keywords
CDU (right-wing)	laschet , maassen , cduwahlprogramm , union
SPD (left-wing)	scholz , brueckenlockdown , pimmelgate , spd

Appendix

Table 5: Keywords used to initialise the political seeds.

Panel of Figure 7 — Figure 7: Estimated parameters for the German network: (a) $\mu$ estimated; (b) Excitation coefficients computed on the tweet extraction from May to Oct. 2021.

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Code evolution for link prediction in complex networks

Alexey Vlaskin, Eduardo G. Altmann

School of Mathematics and Statistics & Centre for Complex Systems The University of Sydney, 2026, NSW & Sydney, Australia.

Automated Algorithm Discovery Link Prediction Genetic Programming

Open paper AskPDF arXiv

The problem of predicting links in complex networks appears in different disciplines and has led to a variety of ingenious human-designed methods. We use this rich program space to explore the performance and behavior of automated code-evolution systems tasked to obtain machine-designed methods for link prediction. Despite being trained on limited data, algorithms evolved through code evolution outperform human-designed methods (with an average AUC score of 0.915 vs. 0.783, computed over 580 networks) and show improved computational efficiency, allowing them to be applied to networks with millions of links. The discovered methods follow approaches that have been employed in human-designed methods, but contain key innovations in the selection and combination of node- and link-features. This illustrates the role modern large language models and genetic algorithms can play in algorithmic innovation and scientific discovery more generally.

Abstract

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