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.

Hawkes Processes

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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

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Sep 28, 2026

Do Temporal Link Predictors Need Learned Memory? A Smoothed-Count Baseline with a Handful of Parameters

Many temporal link predictors summarize past interactions through learned node representations. We examine whether simple counts of recurring interaction patterns can provide competitive predictions without learning these representations. We propose a temporal link predictor based on statistical language modelling. It pools transition and co-occurrence counts across sources to predict links that a source has never formed. We smooth sparse estimates using destination frequencies or Kneser-Ney continuation counts. A shared log-linear rule combines these estimates with popularity, source history, and recency, without node embeddings. In our main evaluation, the model achieves the highest MRR among the compared methods on 7 out of 16 datasets from TGB and TGB-Seq. It also outperforms EdgeBank and Base3 on all 16 datasets and the heuristic family on 14. These gains extend to datasets designed to limit repeated edges. With only 9--13 learned parameters, our model provides a simple and competitive baseline for evaluating future neural temporal link predictors.

Lisi Qarkaxhija, Ingo Scholtes

Chair of Machine Learning for Complex Networks Center for Artificial Intelligence and Data Science (CAIDAS) Julius-Maximilians-Universität Würzburg, DE

Link Prediction Temporal Link Prediction

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Oct 4, 2026

Your Temporal Link Predictor Is Blind to Who Is Active: A Missing Factor That Transfers Across Models

An interaction has two parts: someone decides to act, and then chooses whom to act on. Temporal link prediction has concentrated on the second, and we show that it is blind to the first by construction: a standard negative keeps the real source and swaps the destination, and we prove that this cancels the source's activity exactly from the optimal score, so no model trained and evaluated this way is ever rewarded for learning it. Under the harder historical and inductive negatives, whose sources differ, the same factor becomes the dominant signal. We model it with Source Node Activity Modeling (SNAM), a self-exciting event intensity fitted by an exact point-process likelihood to decayed interaction counts the history states already contain; it has fewer than 20 parameters. On their own, never looking at the destination, these parameters beat DyGFormer and TPNet on four of five datasets under historical negatives. Added to the frozen scores of TPNet, TGN, DyGFormer and DSRD, four models of different design, without retraining anything, they raise AP on almost every backbone-dataset pair in both settings, by up to 25 points. Our full model ranks first overall against eleven baselines on 13 datasets and three protocols, and on million-event streams trains an epoch 9-100x faster than TPNet and DyGFormer. We conclude that source activity is a blind spot of temporal link prediction, and a cheap, transferable one to close. Code is available at https://github.com/Erutaner/Your-Temporal-Link-Predictor-Is-Blind-to-Who-Is-Active.

Ji Zhang, Zixin Liu, Yiran Ding +3

Tsinghua University

Temporal Link Prediction Dynamic Graph Learning

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Abstract

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