{"id":"8e1b4002-3444-47c1-b17c-c03c1a56524f","arxiv_id":"2502.09348","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Recurring triangular groups in face-to-face contact networks suppress information spreading, and higher-order (triad-level) transmission strengthens this suppression.","lead":"Analyzing four real-world face-to-face contact datasets, this paper finds that the same three-person groups keep re-forming over time, and that this recurrence slows down the spread of information in a simulated contagion model. The effect grows stronger when group-level (higher-order) transmission is included, suggesting that stable social triangles trap information within a small circle.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Null model destroys edge recurrence as well as triangle recurrence, so the inhibition effect may be driven by repeated pairwise contacts rather than by recurrent triads.","rationale":"The reader's weakest_assumption identifies the same load-bearing concern, and I agree with that assessment. The central causal claim is that recurrence of triangular groups specifically suppresses information spreading, and the key evidence for that specificity is the null-model comparison in Section 5.4. That null preserves per-snapshot edge and triangle counts but simultaneously destroys edge recurrence, triangle recurrence, node activity persistence, and all other temporal correlations. Since triangle recurrence necessarily involves edge recurrence, the real-versus-null difference cannot by itself separate the two mechanisms. The paper's other support does not resolve the confound: the FDM model reproduces group recurrence, but F0 and mu2 are tuned to match the recurrent-group count c, so the model is not an independent confirmation of the triangle-specific mechanism. The paper has clear strengths, including reproducible code and data, consistent results across four datasets, and a conservative use of held-out validation sections, but the title overstates the mechanism without an edge-recurrence control. The proposed edge-event time-shuffling null directly tests whether aggregate edge recurrence alone can produce the observed suppression, and it can be implemented from the deposited data. The conditional verdict remains appropriate: the manuscript should add this control or a statistical equivalent, and should clarify that the FDM extension reproduces rather than independently predicts group recurrence. With those additions, the central claim would be substantially better supported.","tokens_in":18183,"tokens_out":6315,"duration_ms":67039,"concrete_test":"Run a complementary null that shuffles the time labels of individual edge events rather than node labels. For each empirical dataset, collect every edge event (u,v,t), permute the timestamps t among events, and rebuild each snapshot from the re-timestamped events; this preserves the number of edges per snapshot and the total number of contacts per pair (aggregate edge recurrence), while randomizing which triples co-occur as full triangles in the same snapshot. To distinguish triangle recurrence from triangle abundance, perform the same comparison restricted to snapshots with identical triangle counts, or reject shuffles whose per-snapshot triangle counts deviate. If the real-versus-null suppression in rho* (Fig.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 5.4 compares real snapshots with a null model (SI Section II) that randomly relabels interacting nodes within each 10-minute snapshot. This preserves the per-snapshot number of edges and full triangles, but it eliminates every cross-snapshot correlation: a pair of nodes that interacts in many windows no longer does so, and the same is true for triples. The paper interprets the resulting drop in final spreading range rho* as evidence that recurrence of triangular groups suppresses spreading. However, because a recurrent triangle is built from recurrent edges, the null destroys edge recurrence at the same time it destroys triangle recurrence. If repeated pairwise contacts alone localize information and slow spreading, the real-versus-null gap would appear even with no triangle-specific effect. The title claim is therefore not established by Fig. 5 alone. A secondary issue is that the FDM model's reproduction of group recurrence is partly a fit, since F0 and mu2 are tuned to match the total number of recurrent groups c (SI Section I A); this does not invalidate the null-model comparison but weakens the mechanistic story in Section 5.2.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript studies recurrent triangular groups in four face-to-face interaction datasets, proposes an extension of the force-directed motion (FDM) model with similarity forces to reproduce the observed recurrence, and uses a higher-order SIS spreading model to argue that recurrence of triangular groups inhibits information spreading, especially under higher-order interactions. The empirical analysis is backed by an MMCA theoretical treatment, and the authors compare real data with FDM and attractiveness model (AM) simulations and with a null model obtained by random label swapping in each snapshot.","tokens_in":18430,"tokens_out":2257,"duration_ms":25197,"significance":"If the central claim is established, the paper makes a valuable contribution by connecting group-level temporal recurrence to spreading dynamics and by providing a generative model that reproduces several empirical properties. The work uses multiple real-world datasets, includes a theoretical MMCA analysis, and makes code and data available. The main strength is the systematic comparison of real, modeled, and null networks. However, the key causal attribution in Section 5.4 depends on a null model that removes all temporal correlations, not only triangle recurrence, so the specific claim that triangle recurrence is the operative mechanism needs additional support.","major_comments":[{"comment":"The null model randomly permutes node labels within each 10-minute snapshot. This procedure preserves the per-snapshot number of edges and triangles but destroys every cross-snapshot correlation, including edge recurrence, node activity persistence, and duration memory. The paper interprets the decrease in final spreading range rho* as evidence that recurrence of triangular groups inhibits spreading. However, because a recurrent triangle is built from recurrent edges, the null manipulation removes edge-level recurrence at the same time. The observed effect could be driven by repeated pairwise contacts rather than by the recurrence of triangular groups specifically. To support the title claim, the authors should use a control null model that preserves edge recurrence (e.g., by shuffling triangle identities conditional on the repeated edges, or by rewiring triangles while keeping the edge set of each snapshot) or otherwise show that edge-recurrence-only effects cannot explain the gap. Without such a control, the central causal statement in the abstract and conclusion is not established.","section":"Section 5.4 and SI Section II"},{"comment":"The FDM parameters F0 and mu2 are tuned to match the total number of recurrent groups c of the real network, in addition to matching n and l. The main text states that the FDM model 'reproduces' the recurrent group patterns, but this reproduction is partly by construction because the model is fitted to c. This does not invalidate the null-model comparison in Section 5.4, which uses real data, but it weakens the mechanistic claim in Section 5.2 that the FDM model independently predicts group recurrence. The authors should explicitly state in the main text that c is a fitted target, and they should clarify which aspects of the recurrent group patterns (e.g., inter-event time distributions, as in Fig. 2) are genuinely predicted rather than fitted.","section":"SI Section I A and Section 5.2"},{"comment":"The paper does not report error bars or confidence intervals for the empirical-versus-null difference in rho*. Given that the null model is stochastic, the authors should quantify the variance across null realizations (even if only a small number are used) and assess whether the observed suppression is statistically significant for each dataset and for beta_delta = 0 versus 0.3. This would strengthen the conclusion that the effect is robust and not driven by a particular realization or by a single dataset.","section":"Section 5.4 and Fig. 5"}],"minor_comments":[{"comment":"The MMCA equation assumes independence between the states of neighbors at each time step, which is a standard approximation; stating this assumption explicitly would help readers who are not specialists in temporal-network MMCA.","section":"Section 4.2, Eq. (6)"},{"comment":"The notation in the motion equations is slightly unclear: the denominator is written as the square root of (X_j^t - X_i^t)^2 + (Y_j^t - Y_i^t)^2, but the numerator also contains the difference; this is likely a typesetting issue. Clarify the vector form.","section":"Section 3.1, Eq. (2)-(3)"},{"comment":"The caption states that purple lines represent recurrent full triangles and black lines correspond to the first occurrence, but the label 'recurrent' is defined in the main text only later; define it directly in the caption for clarity.","section":"Figure 1 caption"}],"recommendation":"major_revision","confidential_remarks":"The null-model issue is the core concern: the label-swap null destroys edge recurrence and all temporal correlations, so the specific attribution to triangle recurrence is not yet established. The FDM fitting of c is a secondary issue that should be disclosed in the main text. The paper otherwise has solid empirical grounding and a useful model, so I see a clear path to revision. The editor may also want to verify that the authors' code and data deposit (Zenodo) contains the null-model construction scripts, as the reproducibility claim depends on them."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a serious look, but the title overstates what the evidence supports.\n\nWhat's new and good: the paper documents recurrent full triangles in four face-to-face datasets and shows that an extension of the FDM model reproduces the pattern, and that scrambling node labels within each snapshot—which destroys temporal correlations—increases the final spreading range. The data and code are on Zenodo. The MMCA matches the simulations, and the FDM/AM comparison gives the story some breadth. That is real work, honestly presented.\n\nThe soft spot is the null model in SI Section II. Randomly relabeling interacting nodes in each window preserves per-window edge and triangle counts, but it also wipes out every cross-window correlation, including repeated pairwise contacts. Since a recurrent triangle is built from recurrent edges, the real-versus-null gap in rho* could be driven entirely by edge recurrence. The paper's own proposed mechanism—information staying localized among a small cohort that engages in frequent interactions—is really about edges. To attribute the suppression to triangular groups specifically, the authors need a null model that preserves edge recurrence while randomizing which triples recur, or a statistical control.\n\nThe second issue is smaller. In the SI, F0 and mu2 are tuned to match the total number of recurrent groups c, so the FDM's reproduction of the recurrence pattern in Section 5.2 is partly a fit, not an independent prediction. That doesn't invalidate the empirical observation, but the paper should say it plainly.\n\nThese are fixable. The basic finding—that persistent interaction structure inhibits spreading and higher-order contagion amplifies the effect—is probably robust, because the AM baseline with few recurrent groups spreads further. But the specific triangle attribution needs the control.\n\nRecommendation: send it to peer review. A serious referee should ask for the edge-recurrence-preserving null model before the title claim is accepted. I wouldn't cite the mechanism in my own work yet, but the dataset documentation and the FDM extension are useful.","headline":"Recurrent triangles are real and the inhibition effect is plausible, but the null model conflates edge and triangle recurrence, so the title claim needs a control.","tokens_in":18939,"tokens_out":2915,"would_cite":false,"duration_ms":27278,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In face-to-face interaction networks, the recurrence of triangular groups inhibits the spread of information, and the effect grows stronger when higher-order group interactions are present.","keywords":["recurrence of groups","group formation","information spreading","higher-order interactions","face-to-face interaction networks","temporal networks","null model","SIS spreading model"],"falsifier":"Build a null model that reconnects edges so that each pair of people meets with the same frequency as in the real data but the same three-way triangles rarely close; if the spreading range rises back to the real-network level, then pair-level recurrence is the suppressing mechanism and the triangle-level claim is not needed.","tokens_in":17968,"feed_emoji":"🔺","tokens_out":5169,"duration_ms":51320,"temperature":0.7,"pith_summary":"This paper asks what recurring group meetings do to the spread of information in real face-to-face interaction networks. Analysing four datasets from a primary school, a high school, a hospital ward, and a conference, the authors find that the same three-person groups reappear across time windows. They extend a force-directed motion model, in which people move toward similar others in a hidden space, and show it reproduces these recurrent triangular groups and, unlike a baseline attractiveness model, predicts how far an infection or piece of information spreads. By comparing each real network with a null model that keeps the same number of contacts and triangles in every time window but destroys their recurrence, they establish that recurring triangles suppress spreading, and that including three-way (higher-order) infection channels makes the suppression more pronounced.","feed_headline":"Recurring three-person groups slow information spread","feed_subtitle":"When the same three people keep meeting, information stays in a small circle; three-way contact deepens the effect.","key_machinery":"The load-bearing object is the null model: in each aggregated snapshot, the labels of interacting nodes are randomly swapped, so every snapshot retains its exact number of edges and triangles but the same triangle rarely reappears. Comparing the higher-order SIS spreading dynamics, with a pairwise infection rate and a triangular infection rate, on the real snapshots versus the null snapshots isolates the effect of group recurrence; a microscopic Markov chain approach gives a theoretical check on the simulations.","core_discovery":"The central claim is that recurrence of triangular groups—the same three individuals forming a full triangle in multiple aggregated time windows—reduces the final range of an SIS-type spreading process on temporal face-to-face networks. The paper demonstrates this by constructing a null model that randomly permutes the labels of interacting nodes within each snapshot, preserving the number of edges and triangles per snapshot while destroying their temporal recurrence. On all four real datasets, and in networks generated by the extended FDM model, the real or recurrent networks yield a smaller final infection density than the null counterparts; the gap widens when infection can spread through full triangles. The authors interpret this as information being trapped inside repeatedly co-occurring groups, with higher-order interactions deepening the localization.","pith_inferences":["A stricter test would rewire edges to break only three-way closures while preserving each pair's repeat-contact pattern; the authors do not run this test, and the title claim could overstate the role of triangles if edge recurrence alone reproduces the suppression.","The localization mechanism suggests a link to echo chambers: if the same small group repeatedly interacts, information diversity inside that group falls, a testable analogue in social media would measure retweet-group recurrence against reach.","The result implies a network-design principle: information campaigns on campus or workplace networks should target rare, non-recurrent contacts such as newcomers or visitors rather than the dense recurring triangles.","A direct extension would vary triangle-recurrence level systematically in the FDM model, for instance by tuning the similarity-force strength, and map the final spreading range against recurrence rate to confirm a monotone relation without relying on a null model."],"forward_implications":["If group recurrence is as inhibitory as the paper argues, then measures that break up recurring conversation circles—rotating seating, mixing teams—should increase the reach of information without adding new contacts.","Epidemic and rumor models of face-to-face contact should include triangle-level temporal memory; omitting it will overestimate the final outbreak size.","The gap between real and null networks grows with the higher-order infection rate, so interventions that reduce three-way contact are disproportionately effective at containing spread.","The FDM model, once calibrated on recurrence statistics, can serve as a generator of realistic temporal networks on which to pre-test containment strategies."],"supporting_citations":[{"why":"Supplies the FDM model and the four face-to-face interaction datasets; this paper extends it to reproduce recurrent group patterns.","marker":"[11]"},{"why":"Introduces the higher-order SIS or simplicial contagion model used to simulate information spreading on real and synthetic snapshots.","marker":"[12]"},{"why":"Provides the microscopic Markov chain approach (MMCA) used for the theoretical analysis of the spreading process.","marker":"[13]"},{"why":"Shows that the correlation between edge and triangle degrees promotes explosive information spreading, the prior result this work extends to recurrence effects.","marker":"[14]"},{"why":"Introduces the attractiveness model that serves as the baseline; the paper shows it fails to reproduce recurrent group patterns and spreading behavior.","marker":"[9]"}],"fun_headline_variants":["Repeat triangles trap information spread","Frequent three-person circles hinder info flow","Repeated groups choke information diffusion","Recurring triads restrict info spreading","Old groups bottle up information spread"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The null model shuffles the labels of all interacting people in each time window, keeping the number of contacts and triangles the same but wiping out every temporal memory; the claim that recurring triangles—rather than simply repeated pairs or persistent activity—cause the slowdown depends on that shuffling not also removing another factor that matters.","fun_headline_variants_meta":{"raw":{"variants":["Repeat triangles trap information spread","Frequent three-person circles hinder info flow","Repeated groups choke information diffusion","Recurring triads restrict info spreading","Old groups bottle up information spread"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000345,"raw_usage":{"total_tokens":1859,"prompt_tokens":879,"completion_tokens":980,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":495,"completion_tokens_details":{"reasoning_tokens":935}},"tokens_in":495,"tokens_out":980,"duration_ms":8584,"temperature":1.0,"reasoning_tokens":935,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T21:46:48.298166+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Build a null model that reconnects edges so that each pair of people meets with the same frequency as in the real data but the same three-way triangles rarely close; if the spreading range rises back to the real-network level, then pair-level recurrence is the suppressing mechanism and the triangle-level claim is not needed.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the FDM model and the four face-to-face interaction datasets; this paper extends it to reproduce recurrent group patterns."},{"cited_title":"Iacopini, G","cited_arxiv_id":null,"evidence_quote":"Introduces the higher-order SIS or simplicial contagion model used to simulate information spreading on real and synthetic snapshots."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the microscopic Markov chain approach (MMCA) used for the theoretical analysis of the spreading process."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows that the correlation between edge and triangle degrees promotes explosive information spreading, the prior result this work extends to recurrence effects."},{"cited_title":"Starnini, A","cited_arxiv_id":null,"evidence_quote":"Introduces the attractiveness model that serves as the baseline; the paper shows it fails to reproduce recurrent group patterns and spreading behavior."}],"review_version":1}