Relative Intensity of Collaboration (RIC)

• Relative Intensity of Collaboration (RIC) is a normalized metric comparing observed publication ties to expected levels based on overall output.
• Values above 1 indicate preferential, over-intense collaboration, while values below 1 signal under-intensity in partnership networks.
• RIC’s asymmetry and size normalization enable cross-entity comparisons and reveal hidden integration patterns in research networks.

Relative Intensity of Collaboration (RIC) is a size-normalized indicator of collaboration preference in publication networks. In the recent scientometric literature, it is used to measure whether collaboration between two entities occurs more or less frequently than expected given their overall publication activity and the structure of the collaboration network. Across the studies considered here, $\mathrm{RIC}=1$ denotes collaboration “as often as expected” under random mixing, $\mathrm{RIC}>1$ denotes stronger-than-expected collaboration, and $\mathrm{RIC}<1$ denotes weaker-than-expected collaboration. RIC is explicitly asymmetric: $\mathrm{RIC}(X,Y)$ need not equal $\mathrm{RIC}(Y,X)$. Its principal role is to identify preferential ties, structural asymmetries, and integration patterns that are not visible in simple co-publication counts or unbenchmarked collaboration shares (Hladchenko, 4 Jun 2026, Hladchenko, 4 Feb 2026, Hladchenko, 4 Jun 2026).

1. Definition and interpretive logic

RIC is defined in the cited literature as a normalized comparison between an observed collaboration share and an expected collaboration share. Conceptually, it asks whether a focal entity $X$ collaborates with a partner $Y$ more or less often than one would expect from the marginal publication totals of $X$, $Y$, and the network as a whole. This makes RIC a relative measure of collaboration intensity rather than a volume measure. The central interpretive convention is stable across the recent EU studies: $\mathrm{RIC}=1$ corresponds to random mixing, $\mathrm{RIC}>1$0 to over-intensity or preferential collaboration, and $\mathrm{RIC}>1$1 to under-intensity or weaker-than-expected collaboration (Hladchenko, 4 Jun 2026, Hladchenko, 4 Feb 2026).

This logic distinguishes RIC from simple counts of co-publications. A large country or country group can generate many co-authored papers with another large partner simply because both publish heavily. RIC corrects for that size effect. It also differs from raw shares of co-publications, because those shares do not benchmark a tie against what would be expected from both partners’ total activity within the network. In the cited work, RIC is therefore used to diagnose integration patterns, core–periphery structures, and preferential ties rather than to summarize scale alone (Hladchenko, 4 Jun 2026).

A recurrent implication in the literature is that high absolute collaboration volume does not imply high RIC. The EU-focused studies report precisely this pattern for several major partners: collaboration with the USA, the UK, or China can be extensive in absolute terms while remaining at or below the expected level once normalized by network structure. Conversely, a partner can show high RIC with modest counts if it is overrepresented in the focal entity’s collaboration portfolio (Hladchenko, 4 Jun 2026).

2. Mathematical formulations

The studies considered here present RIC as a publication-based, contingency-table-style indicator, but the printed formulas are not identical. All are interpreted as observed-to-expected comparisons under a random-mixing baseline, yet they differ in how the expected component is expressed.

Source	Printed formula	Baseline interpretation
"Bilateral and multilateral international scientific collaboration of EU member states: OpenAlex vs Scopus (2000-2024)" (Hladchenko, 4 Jun 2026)	$\mathrm{RIC}>1$2	Share of $\mathrm{RIC}>1$3 in $\mathrm{RIC}>1$4’s output vs share of $\mathrm{RIC}>1$5 outside $\mathrm{RIC}>1$6
"Evolving scientific collaboration among EU member states, candidate countries and global partners: 2000-2024" (Hladchenko, 4 Feb 2026)	$\mathrm{RIC}>1$7	Observed odds vs expected odds
"Evolution of bilateral and multilateral collaboration of EU-14 countries across disciplines, 2010-2024" (Hladchenko, 4 Jun 2026)	$\mathrm{RIC}>1$8	Share of $\mathrm{RIC}>1$9 in $\mathrm{RIC}<1$0’s output vs global share of $\mathrm{RIC}<1$1

In these expressions, the basic quantities are publication and co-authorship counts. The papers define $\mathrm{RIC}<1$2 or $\mathrm{RIC}<1$3 as the number of collaborative publications involving both $\mathrm{RIC}<1$4 and $\mathrm{RIC}<1$5, $\mathrm{RIC}<1$6 and $\mathrm{RIC}<1$7 as the total number of publications involving each entity, and $\mathrm{RIC}<1$8 as the total number of publications in the analyzed network. The 2026 EU study presents the indicator explicitly in odds-ratio form, reading the numerator as the observed odds that a co-authored paper of $\mathrm{RIC}<1$9 includes $\mathrm{RIC}(X,Y)$0, and the denominator as the expected odds that a paper not involving $\mathrm{RIC}(X,Y)$1 includes $\mathrm{RIC}(X,Y)$2 (Hladchenko, 4 Feb 2026).

Despite the formal variation, the interpretive structure remains constant. Each formulation is meant to indicate whether $\mathrm{RIC}(X,Y)$3 is overrepresented or underrepresented in $\mathrm{RIC}(X,Y)$4’s collaboration profile. The asymmetry of the indicator follows directly from that directional reading. A value such as $\mathrm{RIC}(X,Y)$5 answers a different question from $\mathrm{RIC}(X,Y)$6, because it benchmarks a different focal collaboration profile (Hladchenko, 4 Jun 2026, Hladchenko, 4 Feb 2026).

3. Data models and operationalization

RIC has been operationalized most extensively in recent work on European and international scientific collaboration. The principal datasets in the cited studies are the CWTS in-house version of Scopus and OpenAlex. One study uses Scopus and OpenAlex jointly for 2000–2024, restricting OpenAlex to cited articles only in order to focus on publications integrated into the citation network, reduce noise from uncited or low-impact records, and mitigate incomplete affiliation metadata. Another study uses Scopus articles for 2000–2024, while a discipline-specific study uses OpenAlex on BigQuery and restricts the analysis to cited research articles (Hladchenko, 4 Jun 2026, Hladchenko, 4 Feb 2026, Hladchenko, 4 Jun 2026).

The standard operational unit is the country or country group. The studies distinguish, among others, EU-14, EU-13, EU candidate countries, and major non-EU partners such as Australia, Brazil, Canada, Chile, China, India, Japan, Norway, Russia, South Africa, South Korea, Switzerland, the UK, and the USA. In the group-based analyses, an entity $\mathrm{RIC}(X,Y)$7 can be a country group rather than a single country, and the corresponding counts are defined over publications involving any member of that group. When a focal country belongs to an aggregated partner group, self-collaboration is excluded from the group totals so that the measure reflects cross-country or cross-group collaboration rather than trivial overlap (Hladchenko, 4 Jun 2026, Hladchenko, 4 Feb 2026).

A major operational distinction is between bilateral and multilateral collaboration. Bilateral collaboration is defined as publications involving exactly two countries, while multilateral collaboration is defined as publications with three or more countries in the affiliation list. The same RIC logic is then applied separately to bilateral and multilateral count structures. In the discipline-specific EU-14 study, this procedure is repeated by year, by discipline, by partner, and by focal country; in the broader EU studies it is repeated annually across 2000–2024 or 2010–2024 (Hladchenko, 4 Jun 2026, Hladchenko, 4 Jun 2026).

Methodologically, the OpenAlex-versus-Scopus comparison introduces an auxiliary quantity, $\mathrm{RIC}(X,Y)$8, and reports that OpenAlex, when restricted to cited articles, yields findings broadly comparable to those obtained from Scopus for country-level research collaboration. The same study notes that OpenAlex permits direct computation in BigQuery over the full period, whereas Scopus’s public interface and API are not suitable for full 2000–2024 RIC calculation because of retrieval limits and incomplete affiliation lists in export formats for multi-author papers (Hladchenko, 4 Jun 2026).

4. Empirical regularities in recent collaboration studies

A central empirical result is that RIC values are consistently higher for multilateral than for bilateral partnerships in the EU-wide comparison based on OpenAlex and Scopus. The discipline-specific EU-14 study reports the same directional pattern across six disciplines: bilateral and multilateral RIC both increase from 2010 to 2024, but multilateral RIC grows more strongly, moving from an aggregate value of about $\mathrm{RIC}(X,Y)$9 to $\mathrm{RIC}(Y,X)$0, while bilateral RIC rises from about $\mathrm{RIC}(Y,X)$1 to $\mathrm{RIC}(Y,X)$2. The recent literature therefore associates rising multilateral RIC with the growing importance of large international consortia and infrastructure-intensive collaboration (Hladchenko, 4 Jun 2026, Hladchenko, 4 Jun 2026).

Within Europe, RIC is used to identify a structured hierarchy. One Scopus-based study interprets the European collaboration network as a core–semi-periphery–periphery formation: EU-14 as a stable core, EU-13 as an intermediate cluster, and EU candidate countries as a peripheral but cohesive cluster. In that analysis, EU-14 intra-group collaboration rises from a predicted RIC of $\mathrm{RIC}(Y,X)$3 in 2000 to $\mathrm{RIC}(Y,X)$4 in 2024, EU-13 intra-group collaboration from $\mathrm{RIC}(Y,X)$5 to $\mathrm{RIC}(Y,X)$6, and candidate-country intra-group collaboration from $\mathrm{RIC}(Y,X)$7 to $\mathrm{RIC}(Y,X)$8. The same study reports that $\mathrm{RIC}(Y,X)$9 rises above $X$0 by 2024, whereas $X$1 remains below $X$2, illustrating directional asymmetry and hierarchical embedding (Hladchenko, 4 Feb 2026).

The EU-focused studies also connect temporal changes in RIC to policy cycles. They report peaks or strengthened collaboration intensity during the final years of FP7, intermediate and later stages of Horizon 2020, and the later years of the study period, including 2023–2024. These patterns are interpreted as indicating that EU Framework Programmes may have strengthened collaboration intensity, especially for multilateral collaboration and particularly for less integrated groups such as EU-13 and candidate countries (Hladchenko, 4 Jun 2026, Hladchenko, 4 Feb 2026).

Partner-specific findings reinforce the distinction between volume and intensity. The USA and the UK typically have high collaboration rates, yet bilateral RIC is often below $X$3, indicating large but not necessarily preferential ties. By contrast, Switzerland and Norway often show high RIC despite more moderate collaboration rates, reflecting regional integration and proximity effects. China presents the opposite case: collaboration volume rises sharply in several disciplines, but multilateral RIC frequently remains below the expected level, especially in relation to EU-14 countries. Russia exhibits a more complex pattern. One study reports that multilateral collaboration intensity with Russia declined but remained above the expected level for EU-14 in 2024 and was $X$4 times higher than expected for EU-13, while another notes that collaboration with Russia in physics and astronomy declined after suspension from Horizon Europe in 2022, even though medicine showed rising multilateral intensity (Hladchenko, 4 Jun 2026, Hladchenko, 4 Jun 2026).

Disciplinary analysis adds another layer. Physics and astronomy show the highest multilateral RIC over 2010–2024, while medicine shows the largest increase in multilateral RIC. Engineering, life and environmental sciences, computer science, and social sciences and humanities also show growth, but generally at lower levels than physics and astronomy or medicine. This suggests that multilateral preferential intensity is strongest in fields organized around large infrastructures, global health consortia, or other large-scale international projects (Hladchenko, 4 Jun 2026).

5. RIC-like extensions beyond country co-authorship

The term “Relative Intensity of Collaboration” is not used uniformly outside country-level scientometrics, but several studies define constructs that are explicitly described as close analogues. In "The QIC-Index: A Novel, Data-Centric Metric for Quantifying the Impact of Research Data Sharing" (Frasch, 30 Sep 2025), the paper does not use the term RIC, yet its dataset-level Collaboration component $X$5 is described as a direct, formalized measure of collaboration intensity that can be straightforwardly adapted into a RIC-like metric. The formulation is

$X$6

with a baseline value of $X$7 for a single-author, single-institution dataset. The paper explicitly suggests that one could define $X$8, normalize it by a field-specific average $X$9, or aggregate it to the author level. Those constructions are identified in the paper as natural derivations from the QIC framework rather than as elements already present in the QIC-Index itself (Frasch, 30 Sep 2025).

In the patent-network study "The role of bipartite structure in R&D collaboration networks" (Filho et al., 2019), RIC is again not the paper’s term, but the closest analogue is the institution-level “collaborativeness” metric

$Y$0

supported by the local collaboration ratio

$Y$1

Here $Y$2 is the fraction of an institution’s patents that involve at least one other institution, while $Y$3 weights collaboration frequency by the size of co-patent teams. The paper states directly that, if one needs a formal institution-level RIC, $Y$4 is the closest direct analogue and $Y$5 is the simpler normalized intensity measure (Filho et al., 2019).

A different form of RIC-like reasoning appears in "Calibrated Fair Measures of Measure: Indices to Quantify an Individual's Scientific Research Output" (Tawfik, 2013). That paper does not define RIC, but it proposes a collaboration-size correction for any bibliometric measure: $Y$6 where $Y$7 is collaboration size and $Y$8 is the “maximum real authors” threshold. The paper’s explicit aim is to counter the inflationary effects of giant collaborations on individual metrics. This suggests a collaboration-intensity interpretation based on the ratio between observed team size and a plausible real-team baseline, but that interpretation is an extension of the paper’s calibration logic rather than a named RIC measure in the paper itself (Tawfik, 2013).

Finally, "Making sense of global collaboration dynamics: Developing a methodological framework to study (dis)similarities between country disciplinary profiles and choice of collaboration partners" (Robinson-Garcia et al., 2019) is not an RIC paper, but it supplies a complementary profile-based framework. It uses cosine similarity between disciplinary and partner-profile vectors, separately for domestic publications, bilateral international research collaboration (BIRC), and multilateral international research collaboration (MIRC). The paper explicitly distinguishes BIRC from MIRC and compares their disciplinary and partner distributions, which makes it compatible with RIC-style analyses of bilateral and multilateral collaboration even though it does not benchmark ties against a random-mixing expectation (Robinson-Garcia et al., 2019).

6. Methodological strengths, limitations, and recurrent misconceptions

RIC’s principal strength is size normalization. Because it compares observed collaboration with an expected baseline derived from network participation, it permits meaningful comparison across large and small entities and across partners with very different publication volumes. The recent EU studies repeatedly use this property to reveal structural asymmetries that raw counts obscure, including EU-14’s stronger ties to high-income partners, EU-13’s stronger ties to candidate countries and Russia, and the relative weakness of collaboration with China despite China’s large global presence (Hladchenko, 4 Jun 2026, Hladchenko, 4 Feb 2026).

A second strength is its suitability for longitudinal and policy analysis. Annual RIC trajectories can trace changes associated with funding regimes, geopolitical shocks, and shifts in network composition. The cited studies use RIC to examine the effects of FP7, Horizon 2020, Horizon Europe, Brexit, and the Russo-Ukrainian war. Because the metric is relative to a network baseline, it can show strengthening or weakening preference even when collaboration counts rise more slowly or more quickly than the network as a whole (Hladchenko, 4 Feb 2026, Hladchenko, 4 Jun 2026).

At the same time, the literature emphasizes several limitations. RIC is asymmetric and must be interpreted directionally. It is not field-normalized in the EU studies, so disciplinary differences in authorship norms and internationalization can affect values. Database coverage matters: OpenAlex has substantial affiliation incompleteness, and the cited-only restriction excludes recent uncited work; Scopus results depend on access to the CWTS in-house version rather than the public interface. One Scopus-based study also notes a small-country instability problem and removes Montenegro because very high RIC values were driven by a very small number of co-authored publications (Hladchenko, 4 Jun 2026, Hladchenko, 4 Feb 2026).

Several misconceptions recur in discussions of RIC. The first is to treat it as a synonym for collaboration volume. The studies directly contradict that reading: the USA and the UK can have high collaboration counts but sub-baseline bilateral RIC, while smaller partners such as Brazil, Norway, or Switzerland can have high RIC with lower counts. The second is to assume symmetry. The literature explicitly states that $Y$9 in general. The third is to treat bilateral and multilateral collaboration as interchangeable. In the recent EU analyses, multilateral RIC is usually higher and more policy-sensitive than bilateral RIC, especially in fields organized around large consortia (Hladchenko, 4 Jun 2026, Hladchenko, 4 Jun 2026).

Taken together, these studies establish RIC as a family of network-normalized indicators for measuring collaboration preference relative to an expected baseline. In its standard country-level form, RIC is most useful when the research question concerns over- or under-intensity of collaboration rather than scale alone. In adjacent literatures on data sharing, patent networks, and individual evaluation, RIC-like constructions appear as natural extensions whenever collaboration breadth, collaboration frequency, or collaboration size must be normalized against a baseline rather than counted at face value (Frasch, 30 Sep 2025, Filho et al., 2019, Tawfik, 2013).