{"id":"cc91191c-a96a-43a2-8656-6e7d11fd0468","arxiv_id":"2507.17177","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Temporal degree centrality and a modified temporal independent cascade model best recover ground-truth influence bands in polarized temporal networks, while eigenvector and closeness centralities perform poorly.","lead":"This paper tests six temporal centrality measures on polarized social networks, in simulations and Twitter data from the 2018 Irish abortion referendum, and finds that temporal degree centrality and a modified temporal independent cascade model most reliably sort users into influence bands. The work offers a practical way to track who becomes influential in a polarized community over time, which matters for marketing and for studying information spread.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central validation is circular: synthetic 'true bands' are defined by degree, and the real-world benchmark (T-ICM) is also a candidate method, so no independent test establishes that degree or T-ICM identifies influence bands.","rationale":"The reader's weakest assumption is the circular use of T-ICM as the real-world benchmark. I agree with that, but I think the more fundamental version of the same problem is that the synthetic ground truth—the only place with a non-circular comparison—is itself degree-defined. The BandNet construction labels nodes as influential exactly when they have high degree; this makes temporal degree centrality's success partly self-fulfilling and means the paper never tests the construct its title names, namely influence. If one accepts that high degree is a reasonable proxy for influence in these stylized networks, the synthetic comparison is still informative, and the paper does provide a reproducible pipeline and a useful community-time aggregation tool; I do not classify the issue as misconduct. But the supporting evidence for the strongest claim is weaker than the prose suggests: Tables 2–4 show PageRank at least ties or beats degree in two of three synthetic settings (overall 0.90/0.86/0.88 vs degree 0.90/0.85/0.78), so 'degree performs best' is already an overstatement even before the ground-truth concern. My proposed check would directly test whether degree survives an independent notion of influence; if it does, the circularity objection loses much of its force. Since the reader's verdict of CONDITIONAL already anticipates these problems, my verdict is UNCHANGED, with agreement 'partial': the circular benchmark is identified, but the degree-defined synthetic ground truth is an additional defect that makes the problem more pervasive.","tokens_in":22240,"tokens_out":8152,"duration_ms":90686,"concrete_test":"Use the existing BandNet2/BandNet3 generator to define ground-truth influence bands not by degree classes but by quantiles of average T-ICM cascade size, sweeping rho over, say, {0.005, 0.01, 0.02, 0.05, 0.1, 0.2}; then recompute the balanced-accuracy table comparing only the non-T-ICM centrality measures. If temporal degree centrality no longer attains roughly 0.8–0.9 or is outperformed by PageRank, the synthetic support for the headline is an artifact of degree-defined labels. If degree remains top-ranked across the entire rho sweep, this central concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline claim—that temporal degree and the modified T-ICM 'reliably isolate nodes into their influence bands'—is supported only by two ground truths, and both are contaminated. In the synthetic BandNets, the true bands are constructed directly from node degree (Section 2.3.1: band 1 uses degree 30 or Poisson mean 40, band 2 uses degree 10 or mean 20, band 3 uses degree 2 or mean 5), and nodes move between bands by swapping degrees. Tables 2–4 therefore mostly measure whether degree-based clustering recovers degree classes; they do not establish that those classes are influence bands. In the empirical RT8 analysis, Section 2.4 states 'with T-ICM being used as the true in the empirical networks,' and Section 3.2.1 also treats T-ICM as one of the compared methods, so the reported agreement between degree and T-ICM is pairwise consistency, not validation. The negative claims about eigenvector and closeness centrality are measured against the same degree-defined or T-ICM-defined labels. Additionally, Eq. (3) inserts I in every temporal block, so an infected node persists in all later time-slices; T-ICM cascade size is then heavily aligned with summed temporal degree, making its agreement with degree centrality unsurprising. Hand-set values rho=0.1, 0.08, 0.02 without a sensitivity analysis complete the gap: the empirical conclusion can change with rho. No independent diffusion data is used anywhere.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies how to identify influential users in polarised temporal social networks. It compares temporal centrality measures (degree, closeness, eigenvector, PageRank, Katz) and a modified Temporal Independent Cascade Model (T-ICM) on synthetic 'BandNet' networks with known influence bands, on the RT8 Twitter conversation around the 2018 Irish abortion referendum, and on a configuration-model randomisation of RT8. Centrality scores are clustered into three influence bands using hierarchical clustering, and a Marginal Community Centrality (MCC) is introduced to track community-level influence over time. The paper's central claim is that temporal degree centrality and the modified T-ICM 'reliably isolate nodes into their bands', while eigenvector and closeness centrality do not perform well in polarised networks.","tokens_in":22539,"tokens_out":3757,"duration_ms":40380,"significance":"If the validation were sound, the paper would offer a practical framework for tracking influence in polarised temporal networks: the influence-band aggregation is interpretable, the MCC provides a clean community-level summary, and the systematic comparison across synthetic and real networks is well structured. The authors also correctly identify that temporal centrality in modular networks is understudied relative to static community-aware centrality. However, the current evidence does not independently establish the headline claim: the synthetic ground truth is defined by degree classes, and the empirical benchmark is the very T-ICM method under evaluation. The significance is therefore contingent on replacing or supplementing these validation steps with an independent measure of influence.","major_comments":[{"comment":"The synthetic ground truth is defined directly from node degree: band 1 nodes have degree 30 or Poisson(40), band 2 nodes have degree 10 or Poisson(20), and band 3 nodes have degree 2 or Poisson(5), with band swaps implemented as swaps of degree. Degree centrality is monotone in degree, so the high balanced accuracy of degree centrality (and of T-ICM, which is degree-aligned as discussed below) is guaranteed to a large extent by construction. The tables therefore measure whether degree-based clustering recovers degree classes, not whether those classes are influence bands. Moreover, the claim that degree and T-ICM are the best is not uniform in these tables: PageRank scores 0.88 in BandNet3 versus 0.78 for degree and 0.81 for T-ICM, and PageRank ties degree and T-ICM in BandNet1. The conclusion in Section 4 that 'T-ICM and degree centrality perform the best' needs to be reconciled with these numbers or replaced by a more nuanced statement.","section":"§2.3.1, Tables 2–4"},{"comment":"The real-world validation is circular. Section 2.4 states that T-ICM is used 'as the true in the empirical networks', and Section 3.2.1 treats T-ICM as the benchmark for the other methods. Yet T-ICM is also one of the methods being evaluated, so the balanced accuracy reported in Fig. 14 is pairwise agreement between candidate methods, not agreement with an independent ground truth. The statement in Section 4 that T-ICM is 'a good benchmark' and that degree centrality 'reliably isolates nodes into their bands' on RT8 is therefore unsupported. The paper should either obtain an independent standard (e.g., observed retweet/cascade data on the same network) or explicitly reframe the empirical contribution as a consistency analysis rather than validation.","section":"§2.4, §3.2.1, Fig. 14"},{"comment":"The modified T-ICM in Eq. (3) inserts the identity matrix I into every temporal block, so an infected node remains infected in all subsequent time-slices and attempts to infect neighbours in each later layer. Under this construction, the expected cascade size is heavily aligned with the summed temporal degree of the seed node: a high-degree node in any time-slice gets many infection attempts, and persistence amplifies this effect. This makes the observed agreement between T-ICM and degree centrality structurally unsurprising rather than an independent confirmation. The authors should test a variant without indefinite persistence (e.g., the original Haldar et al. model without inter-layer self-links) and report whether the ranking and band assignments change.","section":"Eq. (3), §2.2"},{"comment":"The infection probability ρ is hand-set to different values per network (ρ = 0.1 for BandNet1, 0.08 for BandNet2/3, 0.02 for RT8) with no sensitivity analysis, so it is not shown that the conclusions are robust to ρ. In addition, the synthetic networks are generated stochastically (configuration model and random rewiring), yet Tables 2–4 report only point estimates of balanced accuracy with no error bars, confidence intervals, or repeated runs. The differences between methods in BandNet3 (e.g., 0.88 vs 0.81 vs 0.78) may be within the sampling noise of a single realisation. The authors should provide ensemble results over repeated network generations and a sensitivity analysis over ρ.","section":"§2.3, §3.1, §3.2, Tables 2–4"}],"minor_comments":[{"comment":"The caption of Fig. 16 refers to the 'original RT8 network', but the surrounding text and the discussion of the configuration model indicate that the figure reports results for the randomised RT8 network; the caption should be corrected.","section":"§3.2.2, Fig. 16"},{"comment":"The text contains the broken phrase 'This is due toThis causes the localization of eigenvector centrality...'; the sentence should be rewritten.","section":"§3.1.3, near Fig. 10"},{"comment":"There is a duplicated word in 'This can can be interpreted as analogous to the matrix M defined in Eq. 1.'","section":"§2.2"},{"comment":"The phrase 'information becomes soiled within communities' should probably be 'siloed' or 'confined'; as written, 'soiled' is likely a typo.","section":"Abstract, §1"},{"comment":"The row labels 'RT8: config.' and 'RT8: original' are terse and should be expanded to 'RT8: configuration model' and 'RT8: original network' to avoid ambiguity.","section":"Table 1"}],"recommendation":"major_revision","confidential_remarks":"The core issue is that both validation strands are contaminated: the synthetic labels are degree-defined and the empirical benchmark is the method under evaluation. This is a fixable problem in principle, but only if the authors add an independent source of ground truth (e.g., real cascade data or a non-degree-based diffusion simulation) or substantially soften the claims. I would not recommend acceptance without one of these changes. The paper otherwise has a clear structure and the MCC aggregation is a useful conceptual addition."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a solid empirical comparison, but the central claim rests on two circular validations. In BandNet, the \"true\" bands are constructed from degree levels, and on RT8 the benchmark is T-ICM, which is itself one of the methods being evaluated. So the paper's headline — that degree and T-ICM identify influence bands best — is not actually tested.\n\nWhat's genuinely new: the BandNet generator with band swaps and rewiring, and the marginal community centrality aggregation. These are simple but practical, and the paper fills a gap in the temporal-centrality literature where community structure is usually ignored. The writing is clear, the real Twitter case study is a nice stress test, and comparing against a configuration model is a good sanity check.\n\nWhere it falls short: first, in the synthetic networks the \"true\" bands are defined by degree cutoffs (band 1 has degree 30 or mean 40, band 2 has degree 10 or mean 20, etc.). Degree centrality is monotone in degree, so it is essentially reading off the labels. The balanced accuracy numbers mostly show that clustering recovers degree classes, not that those classes are influence bands. Second, on RT8, T-ICM is used as the benchmark and is also one of the compared methods. The agreement between degree and T-ICM is pairwise consistency, not validation. The construction of W(rho) in Eq. (3) adds an identity block in each time-slice, so an infected node persists in later slices; that makes cascade size heavily correlated with summed temporal degree, which explains the T-ICM-degree agreement. Third, no error bars or repeated runs are reported, and rho, alpha, epsilon, and the band count are hand-set without sensitivity analysis. Fourth, the conclusion overstates the results: in BandNet3, PageRank scores highest (0.88 vs 0.81 for T-ICM), so the \"degree and T-ICM perform best\" claim is not uniform.\n\nThese are fixable. The paper would be stronger with a non-degree-based ground truth (e.g., simulate cascades with known ground truth and test centrality against realized influence), a sensitivity sweep over rho, and variance reporting. The real-network section needs a benchmark that isn't also a candidate, or at least an explicit framing as method comparison rather than validation.\n\nWho should read it: people working on influence maximization and temporal centrality in polarized networks. It will be a useful reference for the framework, if not for the headline result. I would send it to peer review — the flaws are serious but addressable, and the topic is timely.","headline":"A useful empirical comparison of temporal centralities in polarized networks, but the headline conclusion is not independently tested because both synthetic and real-world ground truths are defined by degree or T-ICM.","tokens_in":23123,"tokens_out":2991,"would_cite":false,"duration_ms":28950,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that temporal degree centrality and a modified temporal independent cascade model can reliably assign users to influence bands in polarised temporal networks, while eigenvector and closeness centralities cannot.","keywords":["temporal networks","polarisation","centrality measures","influence bands","independent cascade model","community structure","balanced accuracy","Twitter politics"],"falsifier":"Build ground-truth influence from observed diffusion in the RT8 data itself — for example, by measuring how many distinct users eventually mention or retweet content originated by each seed user — and compare the resulting band assignments with those of temporal degree centrality. If degree centrality's balanced accuracy against this empirical ground truth is not in the 0.8–0.9 range, or if using a different infection probability in the cascade model changes which method matches, the claim that degree centrality reliably isolates influence bands in real polarised networks fails.","tokens_in":1717,"feed_emoji":"📈","tokens_out":1627,"duration_ms":80830,"temperature":0.7,"pith_summary":"This paper asks who the influential users are in a social network split into opposing communities, and whether their influence persists as the network changes over time. It proposes grouping users into three influence bands — high, mid, and low — and tracking how users move between bands across time-slices. Using synthetic networks with known bands, the authors show that temporal degree centrality and a modified temporal independent cascade model recover the bands with balanced accuracy around 0.8 to 0.9, while eigenvector and closeness centrality score lower and are distorted by community structure. On a Twitter network about the 2018 Irish abortion referendum, the same two methods give band assignments that agree, and eigenvector centrality again behaves poorly. The practical consequence is that simple degree-based measures can serve as reliable proxies for influence ranking in polarised online conversations.","feed_headline":"Degree centrality reliably finds influencers in polarised networks","feed_subtitle":"On synthetic and real referendum networks, degree and a temporal cascade model sort users into influence bands with ~0.9 accuracy.","key_machinery":"The argument is carried by three constructions. First, a layered temporal unfolding of the network — each node at time $t$ linked to itself and to neighbours at time $t+1$ — supplies temporal degree and closeness centrality, while a supra-centrality matrix with identity inter-layer links supplies eigenvector, PageRank, and Katz scores. Second, the benchmark is a modified temporal independent cascade model encoded as an infection-probability matrix $W(\\rho)$ whose diagonal blocks add the identity, so an infected node remains able to spread in later time-slices instead of returning to the susceptible state. Third, influence bands are produced by hierarchical clustering with complete linkage on the centrality scores, with the number of clusters chosen by the elbow method. Performance is measured by balanced accuracy against known bands on synthetic networks and against the cascade-model bands on the real network. The construction of $W(\\rho)$ is the key adaptation: it turns cascade spreading into a weighted multilayer matrix while keeping content persistent across time-slices.","core_discovery":"On the paper's own terms, the central discovery is that in polarised temporal networks, influence ranking should be built on local temporal connectivity rather than global spectral properties. Temporal degree centrality, defined as the normalised number of edges incident to a node over a time interval, and a modified temporal independent cascade model that keeps infected nodes active across time-slices both assign nodes to the correct influence bands with balanced accuracy near 0.9 in the simplest synthetic network and near 0.85 when degrees are Poisson-distributed. Eigenvector centrality consistently over-scores one community because its eigenvectors localise in modular networks, and closeness centrality produces unstable bands. The same pattern appears in the real RT8 Twitter network, where the modified temporal independent cascade model is used as the benchmark: degree, Katz, and closeness agree with it, while PageRank diverges. The paper concludes that the cascade model and degree centrality reliably isolate nodes into influence bands, and that eigenvector and closeness centralities are not appropriate for polarised networks.","pith_inferences":["Because the temporal independent cascade model is both the benchmark and one of the evaluated methods on the real network, the real-world comparison is only as strong as the assumption that cascade dynamics with $\\rho=0.02$ mirror true influence; testing with other infection probabilities or with observed retweet cascades as ground truth would settle whether degree centrality genuinely outperforms","The synthetic band-swapping dynamics are restricted to moves between neighbouring bands with fixed band sizes; allowing node turnover, more distant band jumps, or time-varying infectivity could reveal which centrality methods generalise to more volatile settings.","The result suggests a low-cost monitoring tool in practice: streaming temporal degree centrality alone could flag users who cross influence bands in polarised conversations, with expensive cascade simulations reserved for periodic recalibration.","The band-aggregation view could be extended to forecast influence shifts around external events, since the real-network time-slices are already defined by televised debates and the referendum day, making those natural change points for testing predictive accuracy."],"forward_implications":["On synthetic polarised networks with known ground truth, temporal degree centrality and the modified temporal independent cascade model achieve overall balanced accuracy near 0.9 in the simplest network and near 0.85 when degree distributions overlap.","Eigenvector centrality systematically attributes the highest scores to a single community in modular networks, and randomising the network to remove modularity makes it behave better, confirming that community structure is the cause of its poor performance.","Community-level influence can be tracked over time by aggregating marginal node centrality into marginal community centrality, which gives comparable per-community influence scores for the cascade model, degree, and PageRank in balanced synthetic networks.","In the real RT8 network, all methods place only one or two nodes in the top influence band, and the nodes identified differ across methods: the PageRank hub is a highly active canvasser that no other method places in the top band.","The decay of joint community-time scores over early time-slices is shared by the cascade model, degree, closeness, and Katz, while eigenvector-based methods favour the central time-slices instead."],"supporting_citations":[{"why":"Supplies the temporal independent cascade model that the paper modifies by adding persistence of infected nodes across time-slices.","marker":"[69]"},{"why":"Provides the temporal unfolding construction used to compute temporal degree and closeness centrality.","marker":"[51]"},{"why":"Provides the supra-centrality matrix method used for temporal eigenvector and PageRank centralities.","marker":"[52]"},{"why":"Supplies the polarised RT8 Twitter network and its two communities used as the real-world case study.","marker":"[13]"},{"why":"Defines the original independent cascade model that the temporal extension builds on and that motivates the benchmark approach.","marker":"[62]"},{"why":"Supplies the hierarchical clustering with complete linkage used to group nodes into influence bands.","marker":"[72]"},{"why":"Supports the configuration-model randomisation used to test which centrality behaviours depend on community structure.","marker":"[70]"},{"why":"Provides the temporal Katz centrality formula used as one of the compared influence measures.","marker":"[53]"}],"fun_headline_variants":["Temporal degree centrality beats spectral measures in polarized networks","For polarized networks, use temporal degree not eigenvector centrality","Influence ranking in polarized networks: temporal degree wins","Local connectivity outperforms global centrality in polarized networks","Temporal cascade model and degree centrality sort influencers accurately"],"cache_read_input_tokens":25088,"weakest_assumption_plain":"The load-bearing premise is that the modified temporal independent cascade model with infection probability $\\rho=0.02$ correctly represents influence spread on the RT8 Twitter network, so its band assignments can serve as ground truth; if that model is wrong, the real-world conclusion that degree centrality performs best has no support.","fun_headline_variants_meta":{"raw":{"variants":["Temporal degree centrality beats spectral measures in polarized networks","For polarized networks, use temporal degree not eigenvector centrality","Influence ranking in polarized networks: temporal degree wins","Local connectivity outperforms global centrality in polarized networks","Temporal cascade model and degree centrality sort influencers accurately"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00099,"raw_usage":{"total_tokens":4207,"prompt_tokens":965,"completion_tokens":3242,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":581,"completion_tokens_details":{"reasoning_tokens":3176}},"tokens_in":581,"tokens_out":3242,"duration_ms":24693,"temperature":1.0,"reasoning_tokens":3176,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T14:54:58.680542+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Build ground-truth influence from observed diffusion in the RT8 data itself — for example, by measuring how many distinct users eventually mention or retweet content originated by each seed user — and compare the resulting band assignments with those of temporal degree centrality. If degree centrality's balanced accuracy against this empirical ground truth is not in the 0.8–0.9 range, or if using a different infection probability in the cascade model changes which method matches, the claim that degree centrality reliably isolates influence bands in real polarised networks fails.","supporting_citations":[{"cited_title":"Temporal cascade model for analyzing spread in ev olving networks","cited_arxiv_id":null,"evidence_quote":"Supplies the temporal independent cascade model that the paper modifies by adding persistence of infected nodes across time-slices."},{"cited_title":"Temporal node centrality in complex networks","cited_arxiv_id":null,"evidence_quote":"Provides the temporal unfolding construction used to compute temporal degree and closeness centrality."},{"cited_title":"Eigenvector-based centrality measures for temporal networks","cited_arxiv_id":null,"evidence_quote":"Provides the supra-centrality matrix method used for temporal eigenvector and PageRank centralities."},{"cited_title":"Find ing polarized com- munities and tracking information diffusion on twitter: a network ap proach on the irish abortion referendum","cited_arxiv_id":null,"evidence_quote":"Supplies the polarised RT8 Twitter network and its two communities used as the real-world case study."},{"cited_title":"Maximizing the spread of influence through a social network","cited_arxiv_id":null,"evidence_quote":"Defines the original independent cascade model that the temporal extension builds on and that motivates the benchmark approach."},{"cited_title":"An introduction to statistical learning: With application s in python","cited_arxiv_id":null,"evidence_quote":"Supplies the hierarchical clustering with complete linkage used to group nodes into influence bands."},{"cited_title":"Ran dom graphs with arbitrary degree distributions and their applications","cited_arxiv_id":null,"evidence_quote":"Supports the configuration-model randomisation used to test which centrality behaviours depend on community structure."},{"cited_title":"Commu- nicability across evolving networks","cited_arxiv_id":null,"evidence_quote":"Provides the temporal Katz centrality formula used as one of the compared influence measures."}],"review_version":1}