{"id":"79c97772-6b0a-4634-aa3f-ef4a9ae07937","arxiv_id":"1908.10667","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The paper defines edge-level betweenness, closeness, and eigenvector centralities plus a decomposition into ranked webs, and applies them to model, social, and epileptic brain networks.","lead":"Researchers adapt vertex centrality measures (betweenness, closeness, eigenvector) to rank the importance of edges in complex networks and introduce a decomposition method that groups edges into ranked sets called webs. The method is tested on model networks, the karate club social network, and brain networks recorded during an epileptic seizure.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The epilepsy web localization may be an artifact of setting adjacent-edge distance to zero in the closeness centrality used for the web decomposition (Sec. II, Eq. 4; Fig. 13).","rationale":"The reader's weakest assumption correctly identifies the zero-distance convention as the key threat to the epilepsy claim. I considered the single-patient limitation, but that affects generalizability rather than internal validity; the zero-distance convention could invalidate the finding even for the reported patient. The synthetic and karate club results are not decisive because they could be consistent with the convention's bias; the epilepsy figure is the only claimed demonstration of practical utility. The proposed test directly perturbs the assumption and would settle whether the SOZ result is robust. The test is feasible because the network construction is fully specified in Sec. IV.B, so the authors can rerun the analysis without new data collection. I therefore agree with the reader's conditional verdict and recommend no change.","tokens_in":18039,"tokens_out":9730,"duration_ms":104044,"concrete_test":"Recompute the CC_e-based web decomposition and the most-important-edge stability analysis for the epilepsy data (Fig. 13) with Eq. (4) modified so that adjacent edges are assigned distance 1 instead of 0, keeping the same weighted path-length rule for non-adjacent edges and identical preprocessing, windowing, and aggregation. Quantify the overlap of the rank-1 web and of temporally stable edges with the seizure onset zone. If the overlap is no longer near or within the SOZ, or drops to chance relative to a sensor-label-permutation null model, the reported localization is an artifact of the zero-distance convention.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Sec. II, the authors define the distance between two edges that share a vertex as d_ij := 0, both for binary and weighted networks. This enters Eq. (4), edge closeness centrality, via the denominator sum of all pairwise edge distances in the line graph. With this convention, every edge incident to a high-degree vertex receives zero contribution from all other edges sharing that vertex, so closeness is inflated roughly in proportion to the local degree/strength of its endpoints. The CC_e-based decomposition then peels off low-closeness edges, so the surviving rank-1 web is structurally biased toward star-like subgraphs centered at high-degree vertices, exactly the structure the authors report for all synthetic topologies (Sec. III.D) and for the karate club (Fig. 10). The epilepsy analysis in Sec. IV.B uses the CC_e-based web (Fig. 13, lower panel); the claim that temporally stable web edges point to the SOZ therefore may be a restatement of the fact that SOZ sensors are high-degree/strength in the functional network, rather than evidence about seizure dynamics. The paper's own caveat ('these findings need to be validated on a larger database', Sec. IV.B) addresses sample size, but not this definitional dependency. If the convention were changed to the standard line-graph distance (d_ij = 1 for adjacent edges), the decomposition and the SOZ overlap could change substantially. This is the most load-bearing unexamined assumption for the paper's headline application.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes edge-level analogues of three standard vertex centralities—betweenness, closeness, and eigenvector centrality—and introduces an iterative 'web decomposition' that partitions the edge set into importance-ranked layers. The methods are tested on synthetic small-world, scale-free, and random networks, on Zachary's karate club, and on evolving functional brain networks of one epilepsy patient. The main reported findings are that important edges tend to connect important vertices, that edge centralities highlight topology-specific structures (including star-like webs), and that in the epilepsy case the most temporally stable important edges and the rank-1 web point to sites near or within the seizure onset zone.","tokens_in":18353,"tokens_out":9423,"duration_ms":104271,"significance":"If the proposed edge centralities and the web decomposition are well defined and reproducible, the paper offers a practical toolbox for edge-level network analysis, and the epilepsy application would be a clinically interesting illustration. The algorithmic decomposition into importance-ranked webs is a useful extension, and the synthetic experiments are systematic across model families and weight settings. However, the central definition of edge closeness is ambiguous or inconsistent as written, and the headline epilepsy conclusion rests on a single patient and on the unexamined zero-distance convention; with these unresolved, the significance of the reported findings is currently uncertain.","major_comments":[{"comment":"As written, the convention d_ij := 0 for adjacent edges makes the edge-closeness measure ill-defined. Under the usual additive shortest-path definition, any two edges connected by a chain of adjacent edges then have zero distance, so the denominator in Eq. (4) vanishes for every edge in a connected component. The paper nevertheless reports finite CC_e values, which means that some other computational convention must be used implicitly. Please state precisely how edge distances are computed, and explain the motivation for setting adjacent-edge pairs to zero. This is not a cosmetic point: all closeness-based results, including the web decomposition in Figs. 8, 10, and 13, depend on this choice.","section":"Sec. II, Eq. (4), definition of d_ij"},{"comment":"The core application claim—that temporally stable edges and the rank-1 CC_e-based web point to the seizure onset zone—is supported by a single patient and by no inferential statistics or surrogate controls. With n=1, the apparent localization could reflect patient-specific electrode placement, the chosen centrality convention, or the zero-distance rule, rather than a property of seizure dynamics. The paper's caveat that the findings 'need to be validated on a larger database' addresses sample size but not this definitional dependency. Please add sensitivity analyses under alternative edge-distance conventions (for example, standard line-graph distance) and a degree/strength-preserving null-model comparison, or substantially soften the conclusion.","section":"Sec. IV.B, Fig. 13"},{"comment":"The correlation analyses between edge ranks and vertex ranks are reported without significance tests, confidence intervals, or null models. Because the centrality definitions share construction principles, part of the observed relationship may be mechanical; for closeness, the zero-distance convention ties edge closeness directly to local degree and strength. A permutation test or a rewiring-based null model is needed before concluding that 'important edges indeed connect important vertices' in a nontrivial sense.","section":"Sec. III.A, Fig. 2, Table II"}],"minor_comments":[{"comment":"The sentence 'excluding the pairs with vertex k' is unclear for edge betweenness, since k is an edge; please specify which endpoint pairs are excluded.","section":"Sec. II, Eq. (2)"},{"comment":"The threshold rule in step 3 uses the '<' sign for repeated eliminations within the same iteration, but the interplay between re-computation and tie handling is described only through the example; a short pseudo-code or flow chart would remove ambiguity.","section":"Sec. II, decomposition algorithm"},{"comment":"The expression for the edge density appears to be missing a division sign; it should likely read epsilon = 2E / (V (V - 1)).","section":"Sec. III, network generation"},{"comment":"The claim that there are 'only a few metrics' for edge importance would be strengthened by a brief comparison with existing edge-centrality measures beyond edge betweenness and bridgeness, especially since edge betweenness is a well-established concept.","section":"Sec. I, Introduction"}],"recommendation":"major_revision","confidential_remarks":"The zero-distance convention in Sec. II is more serious than a mere modeling choice: taken literally, it makes edge closeness degenerate. I strongly suggest requiring the authors to give a precise, consistent definition of edge distance and to re-run the closeness-based analyses with a standard convention before acceptance. The single-patient epilepsy study should be framed as illustrative, and the authors should be asked to include at least one control analysis."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear X,\n\nFirst thing to know: this is a solid methods paper with a serious flaw in its headline application. The edge centrality extensions and the web decomposition algorithm are clearly presented, and the synthetic network experiments are systematic (1000 realizations, multiple topologies). The karate club example gives face validity: the most important edges and webs do pick out the two known factions. That part deserves a careful read.\n\nThe soft spot is the zero-distance convention in Eq. (4). They set the distance between two adjacent edges to zero, without justification. In the line graph, adjacent edges normally have distance 1; setting it to zero means an edge's closeness is inflated by the number of edges sharing its endpoints. The CC_e-based decomposition therefore peels off edges based on local degree/strength, and the star-like webs they report for every topology and for the karate club look like a direct consequence of that choice, not a discovery about network structure. The epilepsy application uses exactly this CC_e-based web (Fig. 13, lower panel), so the claim that the most stable web points to the seizure onset zone may simply restate that SOZ sensors are high-strength nodes. The paper's own caveat about validation on a larger database doesn't address this definitional dependency.\n\nOther soft spots: the epilepsy analysis is a single patient; the correlations in Sec. III have no significance testing; and they never compare against existing edge importance measures like bridgeness or edge betweenness beyond what they already cite. No code or data are released, which makes sensitivity analysis hard for readers.\n\nTo be fair, these are fixable. If the authors rerun the decomposition with standard line-graph distance (d=1 for adjacent edges) and show the SOZ result is robust, the paper would be much stronger. Even without that, the web decomposition itself is a reasonable addition to the toolbox and might be useful for edge-community detection.\n\nI would send this to peer review rather than desk reject, but a good referee should push hard on the zero-distance convention and require the sensitivity analysis. The central methods section can survive; the epilepsy conclusion as stated cannot.","headline":"A useful edge-centrality toolbox paper whose headline epilepsy finding likely rests on an unjustified zero-distance convention for adjacent edges in closeness centrality.","tokens_in":18796,"tokens_out":3607,"would_cite":false,"duration_ms":37917,"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":"By transferring three standard centrality measures from vertices to edges and peeling away less central edges layer by layer, this paper shows that important connections—not important nodes—are what localize seizure-relevant interactions…","keywords":["edge centrality","network decomposition","web decomposition","closeness centrality","betweenness centrality","eigenvector centrality","seizure onset zone","evolving functional brain networks"],"falsifier":"A decisive test is to rerun the closeness-based web decomposition on the epilepsy data with the distance between adjacent edges set to 1 instead of 0; if the rank-1 web no longer overlaps the seizure onset zone, the clinical conclusion rests on the zero-distance convention rather than on a network property.","tokens_in":17827,"feed_emoji":"🧠","tokens_out":8788,"duration_ms":84968,"temperature":0.7,"pith_summary":"The paper claims that the standard question of network science—which constituents really matter—can be answered about connections rather than nodes by applying well-known vertex-centrality formulas to edges, treating edges as the units and measuring path lengths between them. It defines edge versions of betweenness, closeness, and eigenvector centrality, and adds a decomposition that repeatedly removes the least-central edges into a hierarchy of \"webs,\" each corresponding to a different level of importance. Across model networks the authors find that highly ranked edges usually attach to highly ranked vertices, yet the two rankings are not interchangeable: different edge centralities often select different top edges, and the webs are typically star-like clusters around central vertices. In the two real-world applications, the most important edges and webs in Zachary's karate club sit around the club's two leaders, and in an epilepsy patient's evolving brain networks they lie near and inside the seizure onset zone—whereas the most important vertices lie elsewhere. The overall claim is that edge-centric importance is a distinct, operational lens for locating the interactions that govern network dynamics.","feed_headline":"Edges reveal the seizure zone that vertices hide","feed_subtitle":"For one epilepsy patient, edge-based centrality ranks connections near the seizure onset zone first, while vertex measures point elsewhere.","key_machinery":"The machinery is the edge adjacency matrix (the line graph whose vertices are the original edges, with two such vertices connected when the original edges share an endpoint) combined with a zero-distance convention: the path length between adjacent edges is set to 0, and for weighted networks path length is the sum of inverse weights. Plugging this adjacency matrix into the standard eigenvector equation, and using the same shortest-path distances in the betweenness and closeness formulas, yields the three edge centralities. The web decomposition then iteratively computes a chosen edge centrality, removes all edges at or below the current minimum into a web, recalculates on the remaining edges, and finally reverses the web order so that the last-removed edges form the rank-1 \"most important\" web. The decomposition is what turns a one-shot edge ranking into a mesoscopic hierarchy of important connection sets.","core_discovery":"On its own terms, the paper's central discovery is that edge centralities defined through the edge adjacency matrix—two edges adjacent if they share a vertex—behave like vertex centralities in many respects but deliver information vertex rankings do not. In weighted small-world, scale-free, and random networks, the top-ranked edge is very often connected to a top-ranked vertex (up to 90% of scale-free realizations, depending on the measure), and edges ranked high by closeness or betweenness are disproportionately traversed by shortest paths; in scale-free networks they connect core or core-periphery vertices. Yet the three edge centralities identify the same top edge in only roughly 20–50% of weighted model networks, so the concept is not redundant. The edge-centrality-based web decomposition produces a bottom-up hierarchy of edge sets that are usually star-like, and in the epilepsy application the temporally stable edges and the rank-1 web point to interactions near and inside the seizure onset zone, in contrast to vertex centralities, which point outside it. This contrast is the strongest evidence the paper offers that edge-level importance is not a corollary of vertex-level importance.","pith_inferences":["The zero-distance convention for adjacent edges is what makes edge closeness reward edges that share a vertex, so the star-like appearance of webs may be an artifact of the measure; testing with adjacent-edge distance set to 1 would separate metric artifacts from network structure.","The epilepsy result rests on a single patient, and the paper does not compare the webs with chance-level surrogates; a multi-patient replication with surrogate networks would be needed before the finding can guide clinical practice.","The web decomposition effectively treats communities as groupings of edges rather than vertices; this could yield a new definition of overlapping communities, since an edge belongs to exactly one web but a vertex can be incident to edges in many webs.","Because the different edge centralities agree on the top edge in only a minority of model networks, any practical use should probably aggregate across centralities or validate the chosen measure against dynamics."],"forward_implications":["If edge centralities capture importance that vertex centralities miss, then studies that rank only vertices—for example brain-network hub analyses—are missing a layer of structure that can point to the clinically relevant region.","The web decomposition supplies a hierarchy of important edge sets, which is useful exactly when the single most important edge cannot be identified unambiguously.","In evolving epileptic brain networks, the most important edge webs localize near and inside the seizure onset zone and in homologous contralateral regions, suggesting a network-based marker for seizure dynamics.","Because the rank-1 web is typically star-like, the method connects edge importance to structures relevant to synchronization and percolation, giving dynamics studies a specific subgraph to analyze.","The methods apply unchanged to binary and weighted networks of any topology; only the number and composition of webs depend on the centrality chosen."],"supporting_citations":[{"why":"Defines edge betweenness in terms of shortest paths between vertex pairs; the baseline metric the paper extends to closeness and eigenvector centrality.","marker":"[31]"},{"why":"Supplies the shortest-path length convention for weighted networks (inverse-weight sum) that the edge distances inherit.","marker":"[35]"},{"why":"Introduces k-core/k-shell vertex decomposition, the peeling model that the web decomposition adapts to edges.","marker":"[41]"},{"why":"Generalizes k-core to weighted s-core decomposition, which motivates the edge-centrality-based peeling.","marker":"[43]"},{"why":"Provides the small-world network model used as one of the three test topologies.","marker":"[46]"},{"why":"Provides the scale-free network model used as a test topology and for the core/periphery analysis.","marker":"[47]"},{"why":"Provides the random network model used as the third test topology.","marker":"[48]"},{"why":"Provides Zachary's karate club data, the social-network benchmark with known leadership structure used to validate the new edge rankings.","marker":"[60]"},{"why":"Prior vertex-centrality analysis of the seizure onset zone in the same epilepsy data; the contrast that motivates the edge-level application.","marker":"[61]"},{"why":"Defines mean phase coherence, the interaction measure from which the evolving functional brain networks are constructed.","marker":"[80]"}],"fun_headline_variants":["Edge rankings pinpoint seizure zone vertices miss","Edge centrality beats vertex metrics for seizure zone","Edge hierarchy reveals hidden seizure zone in brain networks","Important edges, not vertices, mark seizure onset"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that two edges sharing a vertex are at distance zero from each other in the path metric; if that convention is changed, edge closeness changes and the star-like webs—including the seizure-zone localization—may not survive.","fun_headline_variants_meta":{"raw":{"variants":["Edge rankings pinpoint seizure zone vertices miss","Edge centrality beats vertex metrics for seizure zone","Edge hierarchy reveals hidden seizure zone in brain networks","Important edges, not vertices, mark seizure onset"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000837,"raw_usage":{"total_tokens":3627,"prompt_tokens":898,"completion_tokens":2729,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":514,"completion_tokens_details":{"reasoning_tokens":2673}},"tokens_in":514,"tokens_out":2729,"duration_ms":20331,"temperature":1.0,"reasoning_tokens":2673,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:15:08.551014+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive test is to rerun the closeness-based web decomposition on the epilepsy data with the distance between adjacent edges set to 1 instead of 0; if the rank-1 web no longer overlaps the seizure onset zone, the clinical conclusion rests on the zero-distance convention rather than on a network property.","supporting_citations":[{"cited_title":"Kitsak , author L","cited_arxiv_id":null,"evidence_quote":"Introduces k-core/k-shell vertex decomposition, the peeling model that the web decomposition adapts to edges."},{"cited_title":"Eidsaa \\ and\\ author E","cited_arxiv_id":null,"evidence_quote":"Generalizes k-core to weighted s-core decomposition, which motivates the edge-centrality-based peeling."},{"cited_title":"Erd o s \\ and\\ author A","cited_arxiv_id":null,"evidence_quote":"Provides the random network model used as the third test topology."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides Zachary's karate club data, the social-network benchmark with known leadership structure used to validate the new edge rankings."},{"cited_title":"Geier , author S","cited_arxiv_id":null,"evidence_quote":"Prior vertex-centrality analysis of the seizure onset zone in the same epilepsy data; the contrast that motivates the edge-level application."}],"review_version":1}