Attractiveness-Driven Interaction Model

• Attractiveness-Driven Interaction Model is a framework where an attractiveness variable actively influences movement, contact duration, and selection processes across multiple domains.
• It is applied to spatial, temporal, and matching models to reproduce heavy-tailed distributions, scaling laws, and varied interaction dynamics.
• By coupling intrinsic appeal with stochastic processes, the model provides quantitative insights into phenomena such as epidemic spreading, group formation, and bias in online and social systems.

Attractiveness-Driven Interaction Model denotes a family of formal models in which an attractiveness variable changes how agents move, whom they contact, how long interactions persist, which targets receive attention, or how outcomes are evaluated. In the surveyed literature, attractiveness appears as intrinsic social appeal, popularity, pre-click relevance, destination utility, vocal attractiveness, revealed territorial pull, or—within interacting particle systems—as an order-preserving property of a stochastic process. The common structural feature is that attractiveness is not merely descriptive: it enters transition probabilities, force laws, matching rules, regression targets, or coupling conditions, thereby shaping interaction dynamics at individual, mesoscopic, and system-wide scales (Starnini et al., 2013, Alessandretti et al., 2017, Govindaraj et al., 2014, Gobron et al., 2023, Suen et al., 19 Mar 2026).

1. Conceptual scope and recurrent formal roles

The surveyed literature uses the term across several otherwise distinct traditions. In spatial social-contact models, attractiveness slows movement near certain agents and thereby prolongs contacts. In temporal network models, it biases who receives links from active nodes. In matching models, it changes mutual acceptance probabilities or pair-formation rates. In ranking and click models, it is the pre-click probability that an item will be chosen. In affective computing, it becomes a target variable inferred from multimodal signals. In regional network analysis, attractiveness is operationalized as revealed inflow into a node. In interacting particle systems, by contrast, attractiveness refers to monotonicity under a coupling rather than to social or perceptual appeal (Starnini et al., 2014, Jia et al., 2015, Calò et al., 2024, Gulati et al., 16 Apr 2025).

Domain	Attractiveness variable	Interaction effect
Face-to-face and group formation	intrinsic attractiveness $a_i \in [0,1]$	slows motion and stabilizes contacts
Activity-driven temporal networks	attractiveness $b_i$	biases target selection
Matching and mate choice	scalar attractiveness or $w_{ij}=a_i b_j$	governs acceptance or pair formation
Pedestrian and walk models	$C_a/C_r$ or control parameter $y$	changes clustering or search regime
Search, media, and affective AI	$\theta_d$, vocal attractiveness, image attractiveness	changes clicks, ranking, or engagement
Interacting particle systems	attractiveness as monotonicity	discrepancies do not increase

This breadth of usage suggests that “attractiveness-driven” is best understood as a modeling pattern rather than as a single canonical equation. The pattern is stable: a latent or observed attractiveness quantity is coupled to interaction propensity, persistence, or evaluation. What changes across domains is the semantics of attractiveness and the mathematical object to which it is attached.

2. Motion, proximity, and spatial aggregation

A foundational line of work models face-to-face contact networks through random motion in physical space combined with attractiveness-driven pausing. In the 2013 formulation, agents move in a square domain with periodic boundary conditions and enter conversation when their distance is within $d$. If $\mathcal{N}_i(t)$ is the set of neighbors of agent $i$ at time $t$, the movement probability is

$b_i$0

With heterogeneous $b_i$1, this minimal rule reproduces heavy-tailed contact durations $b_i$2, long-tailed inter-contact times $b_i$3, broad weight distributions $b_i$4, superlinear strength–degree scaling $b_i$5 with $b_i$6, and sublinear growth of distinct contacts $b_i$7 with $b_i$8. In the constant-attractiveness baseline, the contact-duration law reduces to $b_i$9 with $w_{ij}=a_i b_j$0, so heterogeneity in attractiveness is the mechanism that removes the clear cutoff over the observed range (Starnini et al., 2013).

A closely related 2014 model retains random motion, a closed environment, and the same operational role for attractiveness, but emphasizes multiscale reproduction of individual, group, and collective properties across SocioPatterns deployments. It reproduces broad $w_{ij}=a_i b_j$1, $w_{ij}=a_i b_j$2, $w_{ij}=a_i b_j$3, $w_{ij}=a_i b_j$4, $w_{ij}=a_i b_j$5, and approximately exponential-tailed $w_{ij}=a_i b_j$6, and it suggests a mechanistic relation between strength and attractiveness,

$w_{ij}=a_i b_j$7

The same model is robust to changes in density, activation distribution, and even to a Lévy-flight variant with $w_{ij}=a_i b_j$8 and $w_{ij}=a_i b_j$9 (Starnini et al., 2014).

A 2025 re-examination of the attractiveness-driven interaction model sharpened the group-formation picture. With asynchronous updates $C_a/C_r$0, point-like agents in a $C_a/C_r$1D torus, and the same pausing principle, the stationary average degree at fixed density grows linearly with system size, $C_a/C_r$2, rather than remaining size-independent as in a Random Geometric Graph null. The same study finds no percolation threshold in the attractiveness-driven case, whereas the null model exhibits an RGG transition near $C_a/C_r$3 for $C_a/C_r$4. Most notably, the group-size distribution becomes

$C_a/C_r$5

with an exponent reported as independent of density, while the null model yields exponential or bimodal $C_a/C_r$6 (Mariano et al., 16 Jul 2025).

A different spatial tradition treats attractiveness as a force field generated by destinations or attractions. In pedestrian dynamics, the attraction term is

$C_a/C_r$7

with $C_a/C_r$8 and $C_a/C_r$9, so pedestrians experience long-range pull and short-range exclusion. Using the global efficiency

$y$0

and normalized kinetic energy

$y$1

the model yields free moving, agglomerate, competitive, and coexistence phases. In the 2013 corridor setup, the agglomerate phase disappears above $y$2. The later dissertation generalizes this with social influence via

$y$3

exponentially distributed dwell time with mean $y$4, and dynamic bottlenecks, producing localized jam, extended jam, and freezing regimes (Kwak et al., 2013, Kwak, 2017).

A related but conceptually distinct walk model interprets destination attractiveness as the extent to which a walker follows the shortest path. The attractiveness field is

$y$5

and the control parameter $y$6 interpolates between minimum-displacement motion and a non-minimum update rule. The minimum rule gives Brownian-like behavior, while the non-minimum rule yields a universal Cauchy tail

$y$7

For any $y$8, the large-step tail remains Cauchy, whereas the short-step core reflects the destination distribution $y$9. The radial shell-search intensity for the Cauchy walker scales as $\theta_d$0 (Shinohara et al., 2024).

3. Temporal networks and dynamical processes

In activity-driven temporal networks, attractiveness becomes the probability of being selected by active nodes. Each node $\theta_d$1 has activity $\theta_d$2 and attractiveness $\theta_d$3; when $\theta_d$4 activates, the probability of selecting target $\theta_d$5 is

$\theta_d$6

For random walks on such networks, the continuous-time transition rate is

$\theta_d$7

The stationary class-level occupation is

$\theta_d$8

A central result is that in the instantaneous regime, increasing $\theta_d$9 tends to decrease visitation probability before saturation, because highly attractive nodes are often instantaneous degree-$d$0 targets that do not retain walkers. The mean first passage time is

$d$1

This inverts the hub intuition familiar from static or aggregated networks (Alessandretti et al., 2017).

When the same activity–attractiveness architecture is used for SIS spreading, the epidemic threshold depends jointly on $d$2, $d$3, and $d$4:

$d$5

Equivalently, with $d$6 and $d$7,

$d$8

Heterogeneous attractiveness lowers the threshold relative to the classical activity-driven case, positive $d$9–$\mathcal{N}_i(t)$0 correlations facilitate spreading, and negative correlations hamper it (Pozzana et al., 2017).

Consensus dynamics on the same temporal substrate show an additional symmetry. In the generalized voter/Moran model, the heterogeneous mean-field equation is

$\mathcal{N}_i(t)$1

For pure voter dynamics, the fixation probability of a single seed in class $\mathcal{N}_i(t)$2 is

$\mathcal{N}_i(t)$3

whereas for pure Moran dynamics it is

$\mathcal{N}_i(t)$4

The mapping $\mathcal{N}_i(t)$5 exchanges voter and Moran behavior up to time rescaling, highlighting how temporal attractiveness reverses some static-network intuitions (Moinet et al., 2018).

4. Matching, search, and revealed-choice systems

Networked mate choice provides one of the clearest discrete-choice interpretations of attractiveness-driven interaction. In a bipartite graph with node attractiveness $\mathcal{N}_i(t)$6, an encounter between $\mathcal{N}_i(t)$7 and $\mathcal{N}_i(t)$8 succeeds only under mutual acceptance, with single-encounter probability

$\mathcal{N}_i(t)$9

In this model, the Pearson attractiveness correlation $i$0 among formed couples increases monotonically with average degree and decreases with degree diversity. The fully connected benchmark yields $i$1, whereas sparse networks show weaker assortativity because low-attractiveness individuals who match tend to pair “up.” The probability of failing to be matched decreases exponentially in both attractiveness and degree, and negative degree–attractiveness correlation can even produce $i$2 in sparse regimes (Jia et al., 2015).

A complementary evolutionary model places attractiveness on a bipartite encounter network via link weights

$i$3

A link satisfies the pairing condition when

$i$4

with $i$5 controlling selectivity. The rejection-free event probability is proportional to $i$6. Increasing either mean degree $i$7 or selectivity $i$8 strengthens positive assortative mating and increases the number of mated pairs, given sufficient time. Intergenerationally, offspring attractiveness is drawn from a truncated normal on $i$9 with mean

$t$0

and scale

$t$1

Selection mediated by exclusion from reproduction raises mean attractiveness, but truncation-induced offspring skew balances this pressure so that the response to selection $t$2 approaches $t$3 at equilibrium (Dipple et al., 2016).

In sponsored search, attractiveness is operationalized as pre-click relevance rather than interpersonal appeal. The model estimates ad attractiveness by sharing lexical evidence across ads shown for the same query:

$t$4

Here $t$5 measures how often word $t$6 appears in clicked ads relative to all ads for the query. Multiple clicks are modeled through a last-click-conditioned transition matrix $t$7, post-click satisfaction $t$8, and abandonment parameters $t$9. The model explicitly abandons the sequential scan assumption and allows reverse moves in the click order. Empirically it improves first-click prediction, multi-click sequence prediction, and editorial-relevance AUC over DBN, ICM, PM, and AM baselines (Govindaraj et al., 2014).

At a macro scale, regional economics uses attractiveness as revealed inflow. In the multilayer network analysis of European NUTS2 regions, attractiveness is inferred from eight flow types and measured through in-strength, WANNS, single-layer PageRank, and multiplex PageRank. The multiplex perspective alters rankings relative to single-layer views, with Spearman correlations between single-layer and multiplex PageRank in the range $b_i$00–$b_i$01. For 2010, multilayer Infomap identifies $b_i$02 communities, revealing both national cohesion and cross-border structures such as Czech Republic–Slovakia and Northern Ireland–Ireland (Calò et al., 2024).

5. Affective, multimodal, and platform-mediated interaction

In asynchronous video learning, attractiveness becomes an audience-rated affective variable predicted from speaker-side behavior. The 2026 speaker-centric Emotion AI framework defines vocal attractiveness as the perceived appeal of the speaker’s voice and affective engagement as audience involvement of affect during instructional video consumption. Using only speaker-side cues, two XGBoost regressors are trained: a multimodal model for affective engagement and an acoustic-only model for vocal attractiveness. On speaker-independent test sets, the reported performance is $b_i$03 for affective engagement and $b_i$04 for vocal attractiveness. Acoustic cues are the strongest single modality for engagement, and vocal attractiveness aligns strongly with engagement, with Pearson $b_i$05 for human ratings and $b_i$06 for predicted scores. SHAP analysis identifies $b_i$07, HNR, jitter, and shimmer as major drivers of perceived vocal appeal (Suen et al., 19 Mar 2026).

Image-attractiveness learning reframes the interaction around pairwise judgment. In the DARN framework, each image has a latent attractiveness distribution $b_i$08, and for a pair $b_i$09 the score difference is Gaussian with mean $b_i$10 and variance $b_i$11. Five ordinal labels are produced through four learned decision boundaries. Trained on approximately $b_i$12M judgments over about $b_i$13K side-by-side pairs, DARN reaches $b_i$14 five-way accuracy and DARN-V2 reaches $b_i$15; the SBS-trained DARN-V2 also achieves $b_i$16 binary accuracy on the side-by-side web test data (Ma et al., 2018).

Online social platforms reveal a different interaction mechanism: exposure to attractive content changes both production quality and retention. On Flickr, image beauty is predicted by a deep CNN and aggregated at user level. Beauty is broadly distributed, with $b_i$17, whereas recognition is highly concentrated, with $b_i$18. The platform exhibits a majority illusion in beauty exposure: globally $b_i$19 of users have above-average beauty, but $b_i$20 observe more than $b_i$21 of their neighbors above average. A matched observational design finds that following higher-beauty accounts produces about a $b_i$22 increase in next-week photo beauty, while a large imbalance between one’s own beauty and neighbors’ beauty, defined by $b_i$23, increases inactivity risk by about $b_i$24 to $b_i$25 over the next $b_i$26 weeks (Aiello et al., 2017).

Compatibility modeling with LLMs extends attractiveness into simulated interaction trajectories. In the “interaction-first” framework, personas are converted into LLM agents, conversations are simulated, and compatibility is scored by a reward model or by an observer that extracts individual and external ratings $b_i$27. The paper explicitly includes “mutual attraction signals” in the observer prompt. Under sparse rewards and deterministic decisions, the appendix proves that the stable matching induced by predicted rewards converges to the optimal stable matching as policy approximation error tends to zero. Empirically, on speed dating data the best reported LLM methods reach $b_i$28 and $b_i$29, while on divorce prediction the observer reaches $b_i$30 and $b_i$31 (Shang et al., 4 Dec 2025).

6. Bias, fairness, and conceptual limits

When attractiveness is perceptual rather than relational, it can function as a source of systematic bias. In the MLLM study using $b_i$32 face images corresponding to $b_i$33 individuals with and without beautification filters, attractiveness bias appears in $b_i$34 scenarios, or $b_i$35. On trait scenarios, the attractiveness halo effect is significant in $b_i$36 sentiment-directed cases, or $b_i$37. A representative shift is “Confident vs Insecure,” where beautified faces are labeled “Confident” $b_i$38 of the time versus $b_i$39 for unfiltered faces, a gap of $b_i$40. The attractiveness effect is stronger for female faces in $b_i$41 scenarios, or $b_i$42, and beautification more often amplifies gender and age bias than it reduces them (Gulati et al., 16 Apr 2025).

Other application areas report narrower but related concerns. In the MOOC setting, vocal attractiveness is explicitly described as subjective and potentially sensitive to gender, age, and accent biases; the corpus is drawn from Taiwan’s top three MOOC platforms, the ASR is optimized for Mandarin, and deeper fairness mitigation is not reported beyond subgroup analyses showing no statistically significant performance differences by sex, domain, or length quartiles. In the pedestrian-attraction literature, field validation is explicitly deferred, with future empirical calibration proposed through video-tracked trajectories, joining decisions, dwell times, and local densities (Suen et al., 19 Mar 2026, Kwak, 2017).

A final limitation is terminological. In interacting particle systems, “attractiveness” has a technical meaning that differs sharply from social appeal or perceptual preference. For general exclusion processes with generator

$b_i$43

attractiveness means monotonicity: ordered initial configurations admit a coupling under which discrepancies do not increase. The necessary and sufficient conditions are the inequalities labeled $b_i$44 and $b_i$45 in the paper, and the authors emphasize that basic coupling is never attractive for this class except in the simple exclusion process. This use of the term preserves the idea that attractiveness constrains feasible interaction paths, but it is mathematically about order preservation rather than preference or salience (Gobron et al., 2023).

Taken together, these literatures portray attractiveness-driven interaction as a broad modeling strategy for encoding asymmetry in who attracts whom, what captures attention, what stabilizes contact, and which outcomes become more likely. The family ranges from random walks in physical space to epidemic thresholds, assortative mating, click sequences, audience engagement, and multimodal bias. The unifying claim is modest but durable: once attractiveness is made endogenous to transition structure, interaction statistics change qualitatively.