PaperlayerView exact revision on arXiv

Source-linked AI summary

Multiplex coupling: Connecting the intellectual base and the topics of a research field

Massimo Aria, Corrado Cuccurullo, Maria Spano

arXiv:2610.21858v1cs.DLstat.ME

TL;DR

Citation-based and topic-based maps can disagree, while separate or merged analyses lose information about that disagreement. Multiplex coupling keeps the layers distinct and relates their clusters; the paper finds complementary information across layers and reports that persistent structures are much less likely to reflect false branching.

  • Problem

    Existing approaches either merge citation and lexical signals or compare maps globally, leaving no method to relate clusters across separate layers and assess robustness and change over time.

    Source: §1 · p. 2, §2.2 · p. 6

  • Method

    Multiplex coupling standardises reference and topic similarities, clusters each layer into roots and themes, links clusters through their cross-tabulation, and follows root relations over time.

    Source: §1 · p. 2, §2.2 · p. 6, §3.3 · p. 12

  • Results

    2.4% of branching roots persisting at every k are false, against 35% among those that do not persist.

    Source: §6.2 · p. 32

  • Takeaways & Limitations

    The authors conclude that reference and topic layers carry complementary information, and that persistent structures should be read first while others remain hypotheses.

    Source: §6.2 · p. 32, §7 · p. 33

    Themes are less stable than roots, and the framework cannot determine which topic source is right when keywords and title-and-abstract themes agree little.

    Source: §6.3 · p. 32

Abstract

from arXiv · show

Two documents can be close because they cite the same works or because they write about the same things, and the two kinds of proximity often disagree. Science mapping reads them in separate maps or merges them, as hybrid clustering does; either way the disagreement is lost. We introduce multiplex coupling, a framework that couples the same documents by their references and by their terms, keeps the two layers separate and analyses their relation. Similarities are standardised against a null model, and the agreement between the layers is measured on random pairs of documents. Consensus clustering partitions each layer into roots, groups sharing an intellectual base, and themes, groups sharing a topic. A test on the roots $\times$ themes table identifies branching roots and convergent themes, and pairs of roots are followed over time. Every structure is reported with its persistence across numbers of neighbours, which on synthetic data identifies most false branching. Applications to Web of Science, Scopus and OpenAlex collections show that the two layers carry largely complementary information, and reveal substantive and methodological bases that have grown into several topics. The framework is implemented in bibliometrix.

1 Introduction

Reference-based and topic-based maps of the same documents often disagree, while existing approaches either inspect them separately or merge their signals. Multiplex coupling keeps the layers distinct and analyses their agreement, cross-layer cluster relations, and evolution over time.

1 Introduction

  • Documents can share cited works or topics, and these proximities often disagree; a map using only one cannot show where it diverges from the other.Hybrid methods can improve partition accuracy, but merging the signals removes information carried by their disagreement.Source: §1 · p. 2

2.1 Citation-based and word-based science mapping

  • Citation- and text-based partitions can differ systematically, but prior comparisons do not identify which clusters relate across maps or which citation clusters span topics.Hybrid clustering combines the signals but loses whether documents share references without topics, or topics without references.Source: §1 · p. 2, §2.1 · pp. 5–6

2.2 Multiplex and multilayer networks

  • Multiplex coupling partitions the same documents separately by references and terms, then tests cross-layer cluster relations and tracks them over time.The framework standardises similarities against a null model and reports how structures persist across neighbour counts.Source: §2.2 · p. 6, Figure 1 · p. 7

3 The multiplex coupling framework

The framework couples the same documents in separate reference and topic layers, then measures their agreement, clusters each layer, links the clusters, and follows root relations over time. It reports persistence across neighbour counts as part of the results.

3 The multiplex coupling framework

  • The framework represents documents in two layers and pursues three goals: measure layer agreement, cluster roots and themes and link them, then compare roots and track their relations over time.Roots are reference-layer groups sharing an intellectual base; themes are topic-layer groups sharing a topic.Source: §3 · p. 7

3.1 Documents and the two layers

  • Each layer connects documents by shared references or terms; the analysis retains the union of each document’s k nearest neighbours and computes both similarities for those pairs.Topic terms may come from keywords or titles and abstracts; references are not weighted, while terms receive inverse-document-frequency weights.Source: §3 · p. 7, §3.1 · pp. 8–9

3.2 Standardisation, association and node indices

  • Similarities are compared with randomized null matrices, and each pair is classified as consolidation, branching, convergence, or detachment according to which layers show closeness.Layer association is measured on sampled document pairs and tested by permuting the topic layer; node indices describe neighbour overlap, balance, and alignment.Source: §3.2 · pp. 9–10, Figure 2 · p. 10

3.3 Roots and themes

  • Weighted neighbour graphs are clustered with consensus across repeated Louvain runs, yielding reference-based roots and topic-based themes.Consensus reweights edges by how often runs co-cluster their documents, helping address run-to-run variation.Source: §3.3 · p. 12

3.4 Links between roots and themes

  • A root–theme link requires an overlap above the adjusted-residual threshold and a minimum document count; multiple links define branching roots or convergent themes.The same cross-tabulation rule classifies both sides, while structures with one link are consolidated and those without links are dispersed.Source: §3.4 · pp. 13–14

3.5 Cohesion and lift

  • Cohesion and lift compare mean cosine similarity with that of two random documents, with lift 1 marking random-level proximity between roots.These measures use all similarities, not only neighbour-graph edges.Source: §3.5 · p. 15

3.6 Pairs of roots, static and over time

  • Pairs of roots are positioned by their reference and topic lifts; their positions classify four relations, and period-specific trends describe how those relations change.Roots are defined on the whole collection, then followed in periods with enough documents; pairs changing area are shown as trajectories.Source: §3.6 · pp. 15–16, Figure 4 · p. 17

3.7 Robustness to the number of neighbours

  • Because neighbour count changes graph density and cluster granularity, the framework reruns analyses at other k values and reports how often links and structures persist.Interpretation rests on links and structures that persist at every tested k.Source: §3.7 · pp. 17–18

4 Empirical application

The empirical application presents the management collection, with two further collections reported in the supplement. In management studies, the reference and topic layers were largely complementary, and persistent links exposed branching bases, convergent themes, and changes in root relations over time.

4 Empirical application

  • The management analysis uses 2,004 of 2,063 Web of Science articles with both references and keywords; Scopus explainable-AI and OpenAlex disinformation collections are reported in the supplement.The collections were selected to vary in field, size, and how cited references are recorded.Source: §4 · p. 18

4.1 The management collection

  • Only 7.4% of neighbour pairs overlap across layers, and random-pair similarity correlation is 0.17; the management collection yields 16 roots, 28 themes, and 36 links, of which 24 persist at every k.Four of nine branching roots and 10 of 12 convergent themes persist at every k; the persistent branching roots include substantive bases and a methodological base spread across topics.Source: §4.1 · pp. 19, 20, 23, Figure 5 · p. 20

4.2 Evolution

  • Among 78 root pairs followed for at least two periods, 34 change area; the five-period R4–R3 pair moves from close in neither layer to close in topics only.The two bases remain distinct in what they cite while coming to address the same subjects; trends based on only two periods are described as fragile.Source: §4.2 · pp. 23, 26

4.3 Sensitivity and stability

  • Neighbour count has the largest sensitivity effect, while restricting to 1,000 most-cited documents changes roots substantially (ARI 0.44) and titles/abstracts yield themes that agree little with keyword themes (0.12).Consensus partitions are more reproducible than single Louvain runs: mean ARI is 0.82–0.94 for roots and 0.76–0.80 for themes, versus 0.47–0.76 and 0.43–0.44 respectively.Source: §4.3 · p. 26

5 Validation on synthetic data

Synthetic collections with planted roots, themes, and cross-links test recovery and false branching. Roots are recovered more reliably than themes, while persistence across neighbour counts helps distinguish false branching from structures worth interpreting.

5.1 Design

  • The synthetic design crosses six reference groups with seven topic groups, planting branching in R3 and T7 and convergence in T5, with controlled group sizes, noise, and balance.Documents draw references and terms from group-specific pools plus shared global pools; the design includes 54 collections across three sizes, three noise levels, and balanced or unbalanced groups.Source: §5.1 · pp. 27–28

5.2 Recovery of roots, themes and structures

  • Root recovery remains near-exact across designs (mean ARI at least 0.97), while theme agreement falls to 0.65 and 0.54 at highest noise in balanced and unbalanced designs.R3 is found in every run, but T5 is missed in 22% of highest-noise unbalanced runs and diffuse T7 is the hardest planted structure to recover.Source: §5.2 · p. 28, Table 6 · p. 28
  • Only 2.4% of branching roots persisting at every k are false, versus 35% of nonpersistent roots; requiring persistence removes 75% of false branching at a cost of 12% of true branching.False branching arises when an unstable theme splits, and persistence is the diagnostic that supports reading persistent structures first and treating others as hypotheses.Source: §5.2 · p. 29

5.3 Link rules and pairs of documents

  • The adopted link rule retains links from large roots, but document-pair labels for branching and convergence are unreliable, supporting conclusions from cluster-level structures instead.A stricter minimum-share rule halves false branching in the unbalanced design but reduces management links from 36 to 19; single-pair labels match planted branching in 0.35–0.45 of cases and convergence in 0.10–0.32.Source: §5.3 · pp. 29–30, Table 7 · p. 30

6 Discussion

The discussion argues that references and topics provide complementary views of a field, and that their disagreement can reveal structures lost by combining the layers. It treats persistence across neighbour counts as a way to distinguish robust structures while noting limitations in topic stability, data coverage, and temporal analysis.

6 Discussion

  • Across all three collections, correlations between reference and topic similarities on random document pairs are positive but low, at 0.04–0.17.The authors interpret the layers as carrying largely complementary information.Source: §6 · p. 30

6.1 What the second layer adds

  • Branching roots capture one intellectual base applied to different subjects, while convergent themes capture one subject reached from different bases.The management collection’s largest root shares bibliometric-review methods across unrelated subjects; patents and technology indicators are reached from economics of public science and technology forecasting.Source: §6.1 · p. 31

6.2 Robustness as part of the result

  • Consensus clustering raises agreement between theme-clustering seeds from 0.43–0.44 to 0.76–0.80, while the appropriate neighbour count k remains externally determined.Because different k values yield partitions of different granularity, the framework reports persistence across k rather than treating one choice as definitive.Source: §6.2 · p. 31
  • 2.4% of branching roots persistent at every k are false, versus 35% of the others, making persistence the strongest protection against false branching.The authors recommend reading persistent structures first and treating nonpersistent ones as hypotheses.Source: §6.2 · p. 32

6.3 Limitations

  • Themes are less stable than roots: single-run agreement is 0.45 for management themes versus 0.74 for roots, and unstable themes underlie reported framework errors.The errors include false branching in synthetic collections and convergence that does not persist in the disinformation collection.Source: §6.3 · p. 32
  • Topic-layer results depend on the source: keyword themes and title-and-abstract-term themes agree little (0.12), and the framework cannot determine which is right.Keyword cleaning also relies on analyst-prepared lists.Source: §6.3 · p. 32
  • The framework requires usable cited references: only 1,521 of 2,272 disinformation documents entered analysis, and sources without exported references cannot be analysed.The analysed roots therefore describe only documents whose references are recorded.Source: §6.3 · pp. 32–33
  • Roots defined on the full collection remain intact when splitting over time, while most root pairs in growing fields are followed in only two periods; root names are interpretive aids, and synthetic data do not assess temporal evolution.In management, 15 of 78 root pairs are followed in three or more periods; analysts should inspect a root’s strong references before interpreting its name.Source: §6.3 · p. 33

7 Conclusions

The conclusion presents multiplex coupling as a way to study how reference-based intellectual bases relate to topic-based themes in the same documents. Its analyses identify complementary layers and structures connecting bases and topics, while proposed future work addresses additional layers, temporal root changes, and topic-layer instability.

7 Conclusions

  • Multiplex coupling measures agreement on random document pairs, identifies branching roots and convergent themes through the roots × themes table, and follows relations between roots over time.On synthetic data, planted structures are recovered and false branching associated with unstable themes is identified by its lack of persistence across neighbour counts.Source: §7 · pp. 33–34
  • The analysed collections show low agreement between reference and topic layers, which carry complementary information; observed root pairs can remain distinct in references while converging on the same subjects.The framework’s roots × themes analysis also reveals intellectual bases that have grown into several topics.Source: §7 · pp. 33–34

Future developments

  • Future developments proposed are adding layers, allowing roots to change between periods, and strengthening the topic layer with text-only embeddings.The authors propose embeddings of titles, abstracts, keywords, or full texts so documents without shared keywords may still be close; citation-trained models are excluded to keep references out of the topic layer.Source: §7 · p. 34

Funding Information

The paper reports that it received no external funding.

Funding Information

Data Availability

The management collection and materials for the OpenAlex analyses are made available through bibliometrix and Zenodo. Scopus records cannot be redistributed, but the collection can be rebuilt from its query and identifiers by users with Scopus access.

Data Availability

  • The management collection is distributed with bibliometrix through loadBookDataset(), while OpenAlex collections are deposited in bibliometrix format on Zenodo with keyword-cleaning lists and scripts.The scripts produce every number, table, and figure in the paper.Source: Data Availability · p. 35
  • Scopus records cannot be redistributed; the deposit provides the query, EIDs, and DOIs needed to rebuild the explainable-AI collection with Scopus access.Source: Data Availability · p. 35

Supplementary Material

The supplementary material specifies implementation choices and tests indicators for diagnosing false branching. Persistence is the strongest out-of-sample indicator and the framework uses it as its diagnostic.

S1 Implementation details and recommendations for use

  • The symmetric nearest-neighbour relation keeps a pair when either document selects the other, so documents may have more than k neighbours.Only documents with strictly positive similarity are candidates; ties among the k most similar are broken by document order.Source: S1 Implementation details and… · p. 42
  • Consensus clustering drops neighbour-graph edges supported by less than half the runs and never joins documents that are not neighbours.It stops when edge agreement is binary or after ten iterations; the output is the first run of the last iteration, with run agreement measured by mean adjusted Rand index at the first iteration.Source: S1 Implementation details and… · p. 42
  • For Scopus, reference matching is important because omitting it changes roots almost completely (adjusted Rand index 0.09); analyses should also state the topic source and keyword cleaning.Pairs of roots are more reliable when followed across at least three periods with enough documents in each.Source: S1 Implementation details and… · p. 43

S2 Diagnosis of false branching

  • Theme-run agreement was set aside as an indicator because it described the whole collection and pointed in the opposite direction (AUC 0.15).False branching roots occurred in runs with higher theme agreement.Source: S2 Diagnosis of false branching · p. 43
  • On validation data, persistence below 1 and imbalance below 0.3 flagged 11 of 20 false branching roots and 7 true ones, while adding separation caught more false roots but flagged more true ones.Validation included 72 collections with new seeds; at noise 0.7, a planted theme could split into parts receiving comparable link sizes, so imbalance was not low.Source: S2 Diagnosis of false branching · p. 43, Table S1 · p. 44
  • Persistence alone had the highest out-of-sample discrimination (AUC 0.81, versus 0.80 for separation and 0.69 for imbalance), so the main text uses it as the diagnostic.It follows from the framework’s design rather than from simulation-tuned thresholds; no further rule is implemented in the package.Source: S2 Diagnosis of false branching · p. 43

S3 Further results for the management collection

The supplementary management results list themes and their linked roots, alongside cohesion-based plots of roots and themes. The listed themes include convergent topics and dispersed themes without linked roots.

S3 Further results for the management collection

  • The management collection’s theme table reports characteristic keywords, persistence, and linked roots, while Figure S1 maps roots and themes by cohesion in references and topics.Figure symbols distinguish branching roots and convergent themes, consolidated structures, and dispersed structures.Source: S3 Further results for the management… · p. 44, Table S2 · p. 45, Figure S1 · p. 46
  • The listed convergent themes include servitization and competition (T9), tourism and hospitality (T10), research trends and knowledge management (T11), and virtual worlds (T16).T10 and T16 are marked as persisting; T9 and T11 are not.Source: S3 Further results for the management… · p. 45
  • The table also lists convergent themes on web and Google Scholar (T17) and group decision-making (T19), both marked as persisting.T17 links to R1 and R5; T19 links to R2 and R15.Source: S3 Further results for the management… · p. 45
  • Several listed themes are dispersed and have no linked roots, including law and renewable energy (T22), additive manufacturing (T24), and well-being (T27).The table also includes small dispersed themes on bibliometric mapping (T26) and care (T28).Source: S3 Further results for the management… · p. 45

S4 Sensitivity to the number of neighbours

The sensitivity analysis compares alternative neighbour-graph constructions and examines how partitions change with k. No tested graph construction removes sensitivity, so the framework reports which conclusions persist across k.

S4 Sensitivity to the number of neighbours

  • No alternative graph construction removed sensitivity to k; a consensus across k/2, k, and 2k increased agreement most and had no false branching in simulation, at about three times the computation.Shared-nearest-neighbour clustering stabilised cluster counts but not partitions; restricting the graph to significant pairs did not help and had more false branching.Source: S4 Sensitivity to the number of… · p. 47, Table S3 · p. 47, Table S4 · p. 47
  • As k grows, clusters mostly merge rather than reshuffle, and partitions at different k are largely nested, making k act largely as a resolution parameter.Table S5 measures the share of documents whose cluster at the smaller k falls mostly within one cluster at the larger k.Source: S4 Sensitivity to the number of… · p. 47, Table S5 · p. 48
  • At k = 20, successive Louvain resolutions also yielded nested partitions, with mean share 0.88 for roots and 0.88 for themes.The sensitivity to k at a given resolution is reported separately in Table S6.Source: S4 Sensitivity to the number of… · p. 47, Table S6 · p. 48
  • The framework retains the default graph rather than adopting a costlier construction for a modest gain, and reports conclusions that persist across k.The additional cost is limited to the clustering.Source: S4 Sensitivity to the number of… · p. 48

S5 The explainable AI and disinformation collections

The two additional collections extend the framework to Scopus explainable AI and OpenAlex disinformation, where references and topic terms show little overlap. Both collections reveal field-specific intellectual bases and topic links, though some structures and meetings do not persist across k.

S5 The explainable AI and disinformation collections

  • Across the collections, only 2.3% of neighbour pairs overlap between layers, and roots and themes share less than in management (normalised mutual information 0.10 and 0.11).The collections were analysed with persistence measured at k = 5 and k = 20; their links and clustering agreement are compared with management in Table S7.Source: S5 The explainable AI and… · p. 49, Table S7 · p. 49

S5.1 Explainable AI (Scopus)

  • For explainable AI, similarity between references and topics on random pairs was 0.04 (QAP p = 0.01), while single-run agreement was 0.55 for roots and 0.45 for themes.The analysed Scopus collection contained 3,488 documents after reference and keyword processing.Source: S5.1 Explainable AI (Scopus) · pp. 49–50
  • Reference matching changed the explainable-AI roots substantially (adjusted Rand index 0.09), raising references cited by at least two documents from 8,694 to 16,270.The themes agreed at 0.55 before and after matching; the results use matched references.Source: S5.1 Explainable AI (Scopus) · p. 50
  • The explainable-AI references layer produced 22 roots and its topic layer 29 themes, joined by 50 links; 20 links persisted at every k.Among 231 root pairs, 94 were close in topics only, reflecting vocabulary shared across roots that cite different works.Source: S5.1 Explainable AI (Scopus) · p. 50, Figure S2 · p. 53, Figure S3 · p. 54
  • In explainable AI, persistent branching technical bases feed application themes: visual-explanation roots connect to medical imaging and plant-disease topics, while tree-ensemble roots connect to remote sensing and financial fraud.The conceptual explainability root’s persistent link is to the theme on explainability itself.Source: S5.1 Explainable AI (Scopus) · pp. 50–51

S5.2 Disinformation (OpenAlex)

  • In OpenAlex disinformation, only 1,521 of 2,272 documents entered analysis, because many works lacked recorded references or lost all features used by a single document.The collection uses OpenAlex keywords and concepts; references are identifiers, so reference matching was unnecessary.Source: S5.2 Disinformation (OpenAlex) · p. 56
  • The disinformation collection produced 16 roots and 28 themes connected by 25 links; 15 links persisted at every k, but only 1 of 8 convergent themes persisted.Many small themes were unlinked to roots, and 73 of 120 root pairs were close in neither layer.Source: S5.2 Disinformation (OpenAlex) · p. 56, Figure S5 · p. 59, Figure S6 · p. 60
  • Disinformation roots track distinct disciplinary bases, while the persistent convergent Digital Services Act theme joins technical detection and legal-economic work; the Ukraine-war theme’s convergence was not stable across k.The meeting of critical studies and fact-checking around Ukraine is described as suggestive rather than established.Source: S5.2 Disinformation (OpenAlex) · pp. 56–57

S6 Computing time and comparison with single-layer coupling

The analysis scales from 29 seconds for 2,000 documents to 130 seconds for 10,000. Roots resemble reference-coupling clusters more than themes resemble keyword-coupling clusters; the framework adds the relation between the two partitions.

S6 Computing time and comparison with single-layer coupling

  • 29 seconds for 2,000 documents, 62 for 5,000, and 130 for 10,000; cohesion and lift avoid pair enumeration, and persistence reuses the layers.The timings are for random subsets of a larger OpenAlex disinformation and misinformation collection, with three replicates on an Apple M4 Pro 14-core machine.Source: S6 Computing time and comparison with… · p. 62
  • Roots are close to reference-coupling clusters (normalised mutual information 0.28–0.38), while themes are less close to keyword-coupling clusters (0.10–0.18).The comparisons span the three collections; the themes are communities of the nearest-neighbour graph.Source: S6 Computing time and comparison with… · p. 62
  • The framework’s addition to single-layer coupling is the relation between the roots and themes, not a different partition.Part of the difference between theme and keyword-coupling clusters may come from their graphs.Source: S6 Computing time and comparison with… · p. 62

S7 Implementation in bibliometrix

The framework is implemented in bibliometrix as functions for constructing layers, clustering, assessing persistence, and following root pairs over time. Results can be explored through plots and Biblioshiny, with options for large collections and reproducible runs.

S7 Implementation in bibliometrix

  • Five functions follow the framework’s three phases, with a plotting function; the function arguments and paper defaults are listed in Tables S12 and S13.The example analysis reproduces the management collection apart from keyword cleaning.Source: S7 Implementation in bibliometrix · p. 62, Table S12 · p. 62, Table S13 · p. 63
  • The default n = 1000 selects the 1,000 most cited documents for a quick first analysis, whereas the paper analyses all documents.Source: S7 Implementation in bibliometrix · p. 63
  • The example pipeline constructs layers, clusters roots and themes, tests persistence across k = 5 and 20, then follows root pairs across selected years.The example uses years 2004, 2010, 2015, and 2020; n = NULL analyses all documents.Source: S7 Implementation in bibliometrix · p. 63
  • Randomisation for the null model, QAP test, and consensus clustering is controlled by seed, and the session’s random-number state is restored on exit.Functions add results to the received object, allowing analysis to resume at a later step; for example, multiplexRobustness() reuses the layers and reruns clustering.Source: S7 Implementation in bibliometrix · p. 63
  • Returned objects store cluster and link properties, the roots × themes table and residuals, root-pair lifts, partition agreement indices, document memberships, and excluded-document reasons.Plots can be interactive, and greyscale static plots distinguish structures and trends using shapes and line types as well as colour.Source: S7 Implementation in bibliometrix · pp. 63–64
  • Root names come from strong-reference titles, using collection documents, source reference strings, or OpenAlex; OpenAlex queries require configured credentials and can be disabled.Titles are cached for the R session, and openalex = FALSE uses local information only. Biblioshiny provides the analysis under Coupling > Multiplex Coupling, with interactive plots.Source: S7 Implementation in bibliometrix · p. 64

Related papers

Loading 2610.21858v1…