Multilayer patent citation networks: A comprehensive analytical framework for studying explicit technological relationships

The rights bestowed by patents are only enforceable in the jurisdiction in which the patent was granted. To obtain these rights in more than one jurisdiction, an applicant first files in a single jurisdiction (often their local patent office), starting the clock on the period during which they can file for the same invention in other jurisdictions. For the next 12 months, all subsequent filings can ‘claim priority’ from this initial application and inherit the latter’s filing date as its own for the purposes of examination (provided the same content is covered in the application).

There are two primary modes through which an invention can claim priority from an earlier application: the Paris Convention and the Patent Cooperation Treaty (PCT). The former lays down the guidelines for the treatment of foreign patent applications among the contracting parties, including the time limit on priority claims as described above. The latter, for our purposes here, is effectively an attempt to streamline and harmonise the process of patenting in multiple jurisdictions.⁴⁴4https://www.wipo.int/pct/en/. This process does not result in a patent, but rather a preliminary prior art search report, and allows the applicant to nominate the jurisdictions to which they would like to apply for a patent without having to apply at each office separately. Priority can be claimed from a PCT filing, and PCT filings can themselves claim priority from an earlier filing at a local office.

After a patent application has reached a local office, the applicant may want to fine-tune their claims or even be asked to split the described invention into two separate patent applications.⁵⁵5See, e.g., Paris Convention for the Protection of Industrial Property (1883), Article 4G. The inventor is not able to disclose new information during this process, and thus the claims made by the ‘new version’ of the application must be contained within the scope of the initial disclosure. These subsequent filings may claim the priority date of the initial filings and are referred to as ‘continuing applications’.

Patent families, in general, link patents and applications through their priority filing. The resulting ‘family trees’ can be complex and, as such, several types of families exist (Martinez, 2010, Martínez, 2011). ‘Simple’ patent families (as defined by the EPO for their DOCDB database) each consist of a set of patents and applications that are all linked to the same priority filing. This type of family is the one on which we focus in this work, and we will henceforth drop ‘simple’. As such, families can be made up of sets of documents from several jurisdictions, each of which may contain multiple documents. Other families may only consist of a single application in a single jurisdiction.

Families are the unit of analysis for the current work for two reasons. First, they generally align with what one usually thinks of as a single ‘invention’ (Martínez, 2011) and it is the relationships between inventions that we usually aim to capture with citation data. Second, they link inventions across jurisdictions, and therefore allow the alignment of jurisdiction-specific citation networks and, therefore, the introduction of the multilayer network as a potentially useful analytical, conceptual, and mathematical tool to study technological relationships.

From the perspective of data availability, detail, and volume, the obvious choice of data set for testing the utility of the multilayer framework are those patents granted by the three (historically) largest patent offices, also known as the triadic offices: the USPTO, EPO, and JPO. Further, we wish to take a particularly conservative empirical approach to these initial explorations of the multilayer citation network. To do this, we only consider patent families that have granted members in all layers of interest (‘triadic families’) and only consider citations among these families.⁶⁶6The applicants to these offices, however, may be based outside these jurisdictions.

Theoretically, each office examining these triadic applications has access to the same information regarding prior art, and they share much of what they find with the other two offices, directly or indirectly (Wada, 2020, Petit et al., 2021). For this reason, granted members have all had the same opportunities to link to other (older) families in each layer, maximising potential redundancies between layers in the citation network. The exclusion of families that are not triadic, therefore, is why we think of this analysis as likely to produce very conservative results when compared to those that may be obtained for a network without such exclusions.

We also note triadic patent families are often used as a binary indication of a ‘high-quality’ invention (de Rassenfosse and van Pottelsberghe, 2009, Tahmooresnejad and Beaudry, 2019); after all, the applicants thought it was worth the time and money to patent their invention in three of the largest markets in the world. By this logic, our multilayer network consists exclusively of ‘high-quality’ patent families⁷⁷7Note that this is a very narrow view of patent quality. For a comprehensive discussion, refer to Higham et al. (2021). and excludes much controversial subject matter that are not universally patentable (Biddinger, 2000).

A simplified diagram of a multilayer network of citations between triadic families is shown in Figure 1, with full details of the families included in this example described in Appendix C. Note that the multilayer network that we analyse in this paper treats sub-layers, such as whether a citation has been used in a rejection decision (shown in red in Figure 1), as distinct layers. This results in seven layers in total, as the EPO also provides information about whether a citation originated from the international search report (conducted outside the EPO) or the local search report.

Multilayer networks have received particular attention in the past decade (De Domenico et al., 2013, Kivelä et al., 2014, Boccaletti et al., 2014, Cimini et al., 2019), and the development of mathematical and computational tools for their analysis, as well as their timely application, remains a very active field of research across many domains (Gallotti et al., 2016, Vaiana and Muldoon, 2020, Harvey et al., 2021, Yuvaraj et al., 2021, van der Marel et al., 2021). In this work, we not only suggest that patent citation networks are naturally multilayered, but aim to introduce the multilayer framework to the innovation studies community to promote the timely application of novel computational tools that are currently being developed.

To date, the vast majority of the studies that explicitly place patent citation data into a network setting use a single-layer framework (Von Wartburg et al., 2005, Valverde et al., 2007, Clough et al., 2015, Nakamura et al., 2015, Funk and Owen-Smith, 2017, Wu et al., 2019, Higham et al., 2019, Mariani et al., 2019). That is, there is only one type of link (i.e., a citation) between nodes in the network. This approach often makes practical sense, such as when one lacks citation metadata that may be used to distinguish or ‘colour’ the links, or if only one link type is of interest. However, a multilayer network framework is able to naturally incorporate citation metadata, if it exists, into the network structure.⁸⁸8In a related work, also using triadic patents, Morrison et al. (2014) use a multiplex PageRank to assess the centrality of technology classes where layers are defined by inventor location. However, citation source and context are not considered. As an analogy, let us consider the public transport network of a large city containing several different forms of transport, each with its own network of routes and stations. There are usually many points of overlap between these network layers to allow passengers to transfer between modes of public transport, such as a bus stop at a train station. These transfer points link the different network layers together. From both mathematical and computational perspectives, this kind of network is fundamentally different from single-layered networks, particularly when the different layers are defined by links with very different properties (Aleta et al., 2017, Ibrahim et al., 2021). In the public transport context, these properties can be straightforward, such as speed, price, comfort, or environmental harm, or more computationally complex, such as sensitivity to link removal and amenability to rerouting (De Domenico et al., 2014).

In the domain of patent citation networks, each jurisdiction has a set of applications and patents that each contain a set of citations made to other documents. Each of those citations comes with context (Higham and Yoshioka-Kobayashi, 2022). This context can be whether the prior art was discovered by the examiner, the justification for its addition to the document, the relationship between the citing and citing firms, or any other citation metadata that may be obtained or constructed. For many research questions that rely on information derived from the citation network, this information is important to retain, just as it is important to know whether two nodes in a transport network are connected by a bus, an airplane, or a ferry.

At the same time, every patent is part of a family (even if there is only one member). When families contain members filed in multiple jurisdictions, the citation networks associated with each jurisdiction can be linked, just as a bus may stop at a train station, or a train may stop at an airport. Of course, patent applicants are under no obligation to file for a patent on the same invention in multiple jurisdictions. That is, a node (patent family) may not exist in all layers of the network. Not every bus stop is a train station, nor vice versa. The full patent citation network is a true ‘multilayer’ network in this sense. In this work, however, we focus on the subset of nodes that exist across all three layers of interest (the triadic offices). The justifications for this choice are discussed in Section 2.3. The network we define in this work, therefore, is a special case of a multilayer network wherein the layers are node-aligned (Kivelä et al., 2014). Extensions of this work to a more general multilayer framework are discussed in Section 4.

Multilayer networks share many characteristics of interest that are found in single-layer networks; indeed, much of the early research on multilayer networks involved adapting concepts from single-layer networks to this new framework (Berlingerio et al., 2011, Bródka et al., 2012, De Domenico et al., 2013, Battiston et al., 2014). For our purposes, in order to demonstrate the utility of the multilayer framework, it is necessary to compare the network properties derived in this setting to those obtained from the equivalent, flattened single-layer network, wherein citation metadata is ignored (partially or wholly).

The domain within which we choose to explore differences between the multilayer and single-layer frameworks, in the patent citation context, is community detection. The natural grouping of nodes is one of the characteristic features of real-world networks and plays a significant role in describing the structure of the network at scales between node-level and global-level network statistics (Wasserman et al., 1994, Newman and Girvan, 2004, Fortunato, 2010). Often, innovation researchers are interested in the composition of, and interaction between, close-knit groups of meso-scale objects such as groupings of similar technologies (Lee et al., 2015, Alstott et al., 2017, Balland and Rigby, 2017, Yan and Luo, 2017, Mejia and Kajikawa, 2020), and the application of community detection to the multilayer citation network leaves room for direct comparison between our results and these objects that we usually work with. Lastly, community detection can be applied to both multilayer and single-layer networks, which will allow for comparisons between the resultant communities.

The multilayer citation network we construct is generated by citations made by triadic patents and only includes those made to and by triadic families. For the purposes of the current work, triadic patents are patents granted by one of the triadic offices that have family members, or equivalents, granted by the other two triadic offices. Triadic families, on the other hand, will refer to the full set of documents belonging to a family that contains triadic patents.⁹⁹9Note that this definition is slightly different to that used in previous work, notably Dernis and Khan (2004). Until the year 2000, applications to the USPTO were not published, so it was generally impossible to know whether equivalents were filed in all jurisdictions. This led to a slightly awkward definition (families with equivalents granted by USPTO and applied to EPO and JPO) that was in wide use until sufficient time had passed for USPTO application data to accumulate. A common definition in use currently is those families with equivalents filed at the triadic offices; however, as US applications do not list citations, we restrict this definition further to require a grant at each office. These sets include both applications and patents and may be filed at or granted by offices outside the three triadic offices (provided that they are within a family containing triadic patents).

There are several reasons for choosing this subset of nodes and links to define our network, beyond the aforementioned desire to be conservative in our empirical design. The first is that we require well-defined layers. By restricting the citing patents to those granted by the triadic offices, the links (and, therefore, network layers) are defined by the citation context (e.g., the jurisdiction where it was made and the reason it was added), which isn’t available for many offices. Second, restricting the cited families to those that are also triadic means that there are no cross-layer citations, which significantly simplifies the network from a mathematical perspective. For example, a US triadic patent citing a pre-grant publication that was only filed at the Japan Patent Office would be a cross-layer citation, as the latter node does not exist in the US layer. If, however, this Japanese publication was part of a triadic patent family, we can ‘redirect’ this US-originating citation to the US-granted family member, as this patent covers the same technical content, and the citation can remain within the US citation network layer where it was generated. Third, all triadic offices provide detailed citation data. There is no theoretical reason why citation network layers associated with other countries cannot be added if the data exists, but we deemed the triadic offices to be the best starting point to demonstrate the use of the multilayer framework due to their existing popularity among both applicants and researchers.

In this work, we also wish to demonstrate the importance of citation source and context. During the application and examination process, citations that reach the front page of the patent may be added by one of several parties for a variety of reasons. One problem inherent in this citation metadata is that different offices have different examination guidelines and legal frameworks that inform how prior art is cited (Higham and Yoshioka-Kobayashi, 2022). Further, the way that these differences manifest themselves in the metadata that researchers can access is not consistent across offices or, indeed, across time. For some of the analyses in this work, we broadly group citations at each office into two groups: those that were likely found by the examiner and those that were likely found by the applicant. While these groups are far from perfect,¹⁰¹⁰10This is particularly true for the JPO. However, there is suggestive evidence that applicant citations are more likely to be background art than art that could lead to a rejection of the application (Okada et al., 2018). we do so to illustrate the flexibility of the multilayer network approach—the citations that comprise each layer can be filtered based on the research purpose. This flexibility is discussed in more detail in Section 4. One minor restriction that accompanies this approach is that we require citation metadata to exist for all citing patents. The USPTO only started to include this metadata for granted patents from the start of 2001, so the triadic families we consider in this work are those for which the first US grant was in 2001 or later. All families considered in this work have all of their triadic members granted before April 2020. A histogram of the priority dates of the families that comprise the networks we consider in this work is displayed in Fig. 2.

Most of the data used in this work were obtained from Google Patent Public Datasets.¹¹¹¹11https://tinyurl.com/googlepatentdata (accessed 25/10/2021). However, noting that, at the time of data collection, that data was not complete for citations between Japanese publications (notably, Japanese patents citing published Japanese applications), this data was supplemented by data supplied by the Intellectual Property Institute’s Patent Database.¹²¹²12www.iip.or.jp/e/patentdb/index.html (accessed 25/10/2021). We also make use of Cooperative Patent Classifications (CPCs); for consistency, we assign each family the classifications associated with their first US member, as determined by the USPTO. This data was obtained from PatentsView.¹³¹³13https://patentsview.org/ (accessed 25/10/2021).

To reduce the computational complexity associated with large networks, we prefer to work with a subset of the whole patent family network that nonetheless resembles the structure of the whole. Using a set of obviously technologically related families such as those in a specific technology class or filed by firms in a specific sector may not satisfy this requirement, given the known differences in citation patterns across fields (Alcácer et al., 2009, Higham et al., 2017). To remedy this, we choose the subset of patents assigned to CPC class Y02: “technologies or applications for mitigation or adaptation against climate change.” The Y02 class is always a secondary classification and can be added to patent families from a broad set of technologies, from those aimed at reducing drag on airplanes to those aimed at treating diseases whose impact may be exacerbated by climate change (Veefkind et al., 2012, Haščič and Migotto, 2015). This class (and its subclasses) are commonly used as filters to study patented technological developments within specific domains related to both the mitigation of climate change, such as cleaner transport (Aghion et al., 2016, Barbieri, 2016) and energy production (Sun et al., 2021, Persoon et al., 2020), and our adaptation to the inevitable and wide-ranging environmental challenges we will face in the near future (Dechezleprêtre et al., 2020, Hötte et al., 2021). As such, we believe this technology class comprises a suitable microcosm within which we can effectively demonstrate the application of multilayer network methods to patent citation networks.

The resulting data set consists of a well-defined set of citing families, their CPC classifications, the citations they make,¹⁴¹⁴14We exclude very rare citation types, such as those originating from third parties. and the jurisdiction and context of each citation. A description of the layers considered in this work (which can be aggregated for specific empirical tests) can be found in Table 1.

Before a detailed examination into the kind of information that may be extracted from the multilayer network that is not accessible when using a single layer, it is first important to assess whether there is new information in the multilayer network at all. That is, if there is a high level of redundancy between the information contained in each network layer, then the case for using a multilayer framework is weakened. At the same time, if the layers contain very different structural patterns, then a multilayer framework may not be ideal, and more informative results may be obtained if they are treated as individual single-layer networks instead.

One way of assessing these properties is by measuring the interdependence of each layer, or set of layers, relative to the information that can be found elsewhere in the network. Several measures of interdependence have been proposed in the past (Parshani et al., 2011, Morris and Barthelemy, 2012, Nicosia et al., 2013), many of which take a random walk approach to the level of layer interdependence or ‘coupling’ of layers in the network. In this work, at a high level, we are instead interested in the degree to which the information contained in one network layer can inform us about the information contained in another layer.

To this end, we employ the method introduced by De Bacco et al. (2017) and described in detail for our case in Section A.2. This method is a link prediction exercise, whereby a randomly-selected portion of the target layer or layers $\alpha$ have their link information removed and the remaining information in the network may be used to predict the existence of links. As a baseline, the remaining portion of the $\alpha$ is used as the training set, the receiver operating characteristic (ROC) curve is calculated, and the area under this curve (AUC) is computed. We can then introduce sets of other layers, $\beta$, into the training set, and compare results obtained by adding this information to those of the baseline. If the predictive power (as measured by the AUC) of this augmented set $\alpha+\beta$ is not significantly larger or smaller than the baseline predictive power, then $\beta$ does not contain useful information over and above that contained in $\alpha$. If, however, we note a significant increase in predictive power relative to the baseline, then $\beta$ contains complementary information that cannot be extracted from what remains of $\alpha$.

Much information can be garnered from comparisons of the change in predictive power when $\alpha$ and $\beta$ are interchanged. For example, when the links in one layer are a subset of links in another, then we expect the change in predictive power to be asymmetric when we swap $\alpha$ and $\beta$ — adding the subset to try to predict links in the full set will likely produce worse results than if only the full set was used for training the model. The information in the subset is redundant and could even mislead the model.

When two layers contain complementary information we would expect increases in predictive power regardless of the layer comprising the test set. This complementarity can arise in several ways, such as through similar community structure despite large differences in the specific links that produce these structures. A significance decrease, on the other hand, would indicate that $\beta$ contains information that is irrelevant for the prediction task and actually added noise; this could occur, for example, if the link generation mechanisms were independent of the node properties, or were driven by different node properties in different layers.

Figure 3 shows the results of the interdependence analysis for various $\alpha$ and $\beta$ sets in which we are interested. For graphical simplicity, we focus on the sublayers generated by the USPTO and the complete JPO and EPO layers (where the latter two always include all of their sublayers listed in Table 1). This is done to demonstrate, compactly, the complementarity of information across jurisdictions as well as that of their sublayers, with the most commonly utilised sublayers in the literature (US applicant and examiner citations) as exemplars for the latter calculations.

The results displayed in Figure 3 show that adding more layers increases predictive power across all combinations of $\alpha$ and $\beta$ we considered. This outcome suggests that, while they differ by the amount of unique complementary information they contain, each layer nonetheless contains information that is not available in the other layers. Specifically, information about the missing values in $\alpha$ is more accurately predicted when layers that are not already in $\alpha$ are included in the training set, relative to the sole use of the information that remains in $\alpha$. This is to be expected, as examiners at each office conduct much of their prior art search independently.

A prime example of complementarity is displayed by the US sublayers (US-APP and US-EXM). These layers are almost mutually exclusive,¹⁵¹⁵15Copying occasionally happens due to the recycling of citations for continuing patent applications. but predictive power for links in one layer is significantly boosted when the other layer is added, regardless of which is the test set. That is, there is very little overlap in these layers, and yet one can be successfully used to predict the links in the other, likely due to the similarity of mesoscale network communities within each of these layers.

That some citation types add more information than others is also expected. After all, information sharing occurs regularly between offices (Wada, 2020), and this process leads to the duplication of citations between specific layers. While this sharing happens increasingly through direct collaboration between offices examining equivalents,¹⁶¹⁶16https://www.wipo.int/case/en/. most of the citations we consider here were made before these formal programs were launched. As such, for much of the time period we consider, the information ‘sharing’ likely takes place indirectly, through applicants. For example, the EPO produces a search report for the applicant to consider before a substantial examination takes place. Under their duty of disclosure obligations at the USPTO, it is considered good practice to pass this information on to the USPTO if an equivalent is being examined there simultaneously (which will usually be the case for triadic patent families). This information is submitted via an information disclosure statement and the USPTO examiner then assesses the relevancy of the prior art that is listed on the search report. When it happens at all, only a small percentage of citations from the EPO search report will be used to justify rejection and be recorded as examiner citations, while the remainder will be recorded as applicant citations. As such, the EPO search report is a non-obvious mechanism through which citations are duplicated from EP-SEA citations to US-APP citations (and sometimes to US-EXM citations).

Similarly, while there is a knowledge disclosure obligation at the JPO, the incentives for complying are very weak relative to the USPTO (Nakamura and Sasaki, 2016). However, applicants to the JPO often use in-text citations to make a case for patentability, and perhaps much more so than the typical applicant to the USPTO or EPO. As such, it is plausible that, for triadic patents, these citations are included in-text in other equivalent applications and are therefore easily accessible to examiners in all jurisdictions. If these citations are deemed relevant by multiple examiners, these citations might also appear to be duplicated across network layers.

Having found that the different layers likely contain complementary information, we now investigate the patterns extracted from a multilayer network approach and compare them with those extracted from single-layer networks that exclude citation context. Specifically, we wish to detect communities of triadic families that are similar in their citation patterns. These communities represent mesoscopic structural patterns contained in the networks that are not objectively or directly observed, but can be inferred from the data.

To this end, we apply a community detection algorithm to three networks: i) the (seven-layer) multilayer network containing the EPO, JPO, and USPTO layers (MULTI); ii) the network obtained by flattening all the layers in (i) into a weighted single-layer network and ignoring citation origin and context (ALL-AGG); iii) the weighted single-layer network obtained by flattening the USPTO examiner and applicant layers only (US-AGG). Each link is weighted by the sum of link weights across all layers we consider; that is, if the same family-family citation exists once in each of $n$ layers, then the link is assigned weight $n$. While rare, link weights greater than one can occur within sublayers; for example, when a divisional makes the same type of family-family citation as its parent, the link weight corresponding to this link will be two.

To perform the community detection task, we consider a probabilistic generative model that assigns a probability to a citation between two families that depends on the communities they belong to, as described in De Bacco et al. (2017). In our case we have access to relevant metadata about each triadic family, hence we consider the model of Contisciani et al. (2020), MTCOV, that is also able to incorporate the office at which priority was filed (which is often not a triadic office) as a node covariate to drive inference along with the network structural information. This covariate allows us to incorporate the home-bias of citations in early search reports (Bacchiocchi and Montobbio, 2010) and, to a lesser extent, industrial agglomeration patterns (Asheim and Gertler, 2005) (given the strong correlation between assignee location and priority office), to inform the inferred citation probability alongside explicit network structure. This model automatically balances the weight of the covariates’ contribution in determining the communities. In all our experiments we find that node covariates are indeed significant, in that they allow us to better quantify the probability of certain citation patterns. The optimal number of communities in each case is extracted through a cross-validation procedure, see Appendix A for details. In addition to being able to incorporate a covariate that may inform network structure at scales beyond individual links, MTCOV is scalable to large networks, allows overlapping communities, and is open-source,¹⁷¹⁷17https://github.com/mcontisc/MTCOV all of which are desirable features for the current work.

We chose ALL-AGG as a comparison because it contains all the same links as the multilayer network, and even accounts for link overlap among layers, but without context. As such, any differences in the extracted communities arise solely due to the addition of citation context, and the incorporation of this context into our network model. US-AGG is included in these comparisons as the most common citation network used in previous work. The USPTO also tends to make many more citations per patent, and so this single-jurisdiction layer is likely to be the most ‘complete’, with respect to the links in the full triadic network.

The communities extracted for MULTI are shown for a random subset of patent families in Figure 4. Analogous figures for the ALL-AGG and US-AGG networks can be found in Appendix B. While the model allows for overlapping communities (nodes can belong to multiple communities), in Figure 4 we colour nodes by their ‘hard’ communities, whereby each patent family is assigned to the community to which it displays the highest affinity. The optimal number of communities, calculated via the cross-validation exercise described in Section A.1, was found to be 15 for the multilayer citation network and 7 for ALL-AGG and US-AGG. Finally, the location of the assignee of each patent family (rather than the priority office, which is used as a covariate in the community detection procedure) is indicated by the shape of the node.

Between networks, several graphical observations can be made in the geographic composition of the extracted communities, despite the differing community sizes. First, country-based homophily is very clear. The most obvious example of this is that families filed by Japan-based assignees are primarily grouped with families that are also filed by Japan-based assignees, with the only observable difference between the networks being how many communities are found within this group of families (1 for ALL-AGG and US-AGG, and 5 for MULTI); however, this difference is expected as the optimal number of communities multilayer network is greater. The other consistently geographically-homogeneous communities include those families assigned to German firms and those assigned to South Korean firms. The existence of these groupings is somewhat expected — geographic citation biases are a well-known phenomenon and have a wide range of drivers, including local industry agglomeration, shared language, prior-art search strategies, knowledge spillovers, and coordinated technological development strategies at the national level (Jaffe et al., 1993, Almeida and Kogut, 1999, MacGarvie, 2005, Bacchiocchi and Montobbio, 2010, Wada, 2016). Because priority office information is included in the community detection algorithm, the existence of the kind of geographic grouping we observe reflects that while technological similarity plays a big role in citation linkage at the micro-level, simple geographical metadata can be highly predictive of network structure at larger scales.

One would expect that the citations we consider in this work should link families with technological similarities and, therefore, the communities detected should group inventions with shared and legally relevant technological features. Indeed, the geographical biases in citation linkages that are observed above may be considered to be artifacts of the systems within which technological development occurs, and perhaps even hinder our understanding of the nature of innovation more generally. We assert that the multilayer framework is one way of mitigating some of these biases, as it integrates relevant technological relationships uncovered by several different, and geographically separated, patent agents and examiners working mostly independently. In aggregate, this information should give a more balanced view of technological similarity and down-weight those links that are heavily influenced by unwanted geographical and office-specific biases and conventions. However, the link weights in the ALL-AGG network may play a similar role. As such, we will now turn to the differences in the technological information contained in the three networks and examine the importance of citation context (i.e., source and justification) in assessments of technological similarity.

To do this, we directly compare the network of meso-level technological relationships that can be gleaned from extracted communities with externally-defined technological categories. First, we construct a weighted bipartite (two-mode) network of relationships between the extracted communities and the 3-digit Cooperative Patent Classification (CPC) codes that the families within each community were assigned upon application to the USPTO.¹⁸¹⁸18This choice was made for the sake of consistency. Different offices may make slightly different judgements regarding the particular set of classes assigned to an application. By using data from a single office, we do not have to be concerned with these systematic differences. CPC codes, henceforth referred to simply as classes, were chosen due to their status as the primary classification system at two of the triadic offices and widespread use in research, particularly in studies of technological evolution and forecasting technical change. The weight of each link in the bipartite network between communities and classes is proportional to the fraction of families in each community that were assigned to a given class. We then project onto the technology class nodes to obtain a network of classes wherein links exist between classes that were both found in the same community or communities. A higher link weight between two nodes in this projected network reflects a more similar distribution of those classes across the extracted communities (Vasques Filho and O’Neale, 2018).¹⁹¹⁹19Note that these classes are not directly used in the community detection process. However, the community detection process relies on citation linkages, and these citations are often found through searches within the technology classes to which the application under examination has been assigned (see, e.g., Demey and Golzio, 2020).

We then construct two basic comparison networks: co-classification (Engelsman and van Raan, 1994, Breschi et al., 2003) and inter-class citation linkage (Leten et al., 2007, Alstott et al., 2017). The former contains a link between (3-digit CPC) classes when a family is assigned to both, with weights proportional to the relative frequency of such occurrences. The latter network contains links between these classes with weights proportional to the number of citations made between families that were assigned to each class, normalised to the total made by each of the classes.²⁰²⁰20To compare this network to our (undirected) projected networks, we take the sum of the normalised weights of the directed links between classes to obtain an undirected link weight. This simplification is a necessary evil for the current purpose and may miss some nuance in certain technological relationships. We keep self-loops in this network, as they are required for sensible link-weight normalisation. For example, if class A makes 10 citations (and receives none), one of which goes to a class B family but 9 return to other class A families, this is a very different situation from one in which all 10 go to class B families. Because we normalise link weights by total citations made, ignoring self-citations would give the link from A to B the same weight in both scenarios, rather differing by a factor of 10. Further description of the construction of all networks used in this section can be found in Appendix B.

Now that we have two externally defined, node-aligned class networks, we are able to directly compare their structure to those extracted from the community-class bipartite networks. Because the nodes in each network we wish to compare are labelled and the same for all networks, we are able to use known-node correspondence methods that allow for comparisons at the node-level in such a way that accounts for differences in relationships between specific node pairs and for higher-order relationships (Tantardini et al., 2019). For this exercise, we use two different methods of comparison: the Frobenius norm and DeltaCon (Koutra et al., 2013).

The Frobenius norm is applied to the raw differences in the adjacency matrices between two networks, and thus quantifies the entry-wise (link-level) differences in the matrices being compared. When the networks being compared are unweighted, this distance is simply the square root of the number of pair-wise differences between the networks. However, this method easily accommodates the weighted case, wherein each pair-wise difference can have a magnitude other than unity.²¹²¹21Specifically, the Frobenius norm of a matrix $A_{m\times n}$ is defined as the square root of the sum of the absolute squares of its elements, $$||A||_{F}=\sqrt{\sum_{i=1}^{m}\sum_{j=1}^{n}|a_{ij}|^{2}}\,.$$ (1) The Frobenius norm is a crude comparison method that cannot account for higher-order relationships between nodes, such as the importance of a link in the overall structure of the network, but it is a good heuristic when making multiple comparisons as we do here. DeltaCon, on the other hand, is more sophisticated, and indirectly considers every possible path between two nodes. In this way, differences in the weights of links that are particularly important for the network structure at the macro-level are incorporated into the comparison. While the DeltaCon algorithm can be very computationally expensive on large networks, and an approximation is possible, our class network is small enough (535 nodes) that the exact form can be used (Koutra et al., 2013). Both the Frobenius norm and DeltaCon calculate a distance metric whereby smaller distances indicate more similar networks. These methods are implemented in Python using the numpy (Oliphant, 2006) and netrd packages (McCabe et al., 2021).

In addition to the network comparison methods, we are also able to quantify the diversity of technology classes within each community extracted. For this purpose, we make use of the Rao-Stirling diversity (RSD) (Rao, 1982, Stirling, 2007), which considers both the homogeneity of each community (with respect to the classes within it) and the level of ‘surprise’ that specific pairs of classes are found together. For the latter consideration, we operationalise class distance using the inter-class citation network described above, as citations are what we use to extract the communities in the first place.²²²²22That is, it would be a ‘surprise’ to find a pair of classes that don’t cite each other, but are nonetheless found in the same community. Calculating this index for all communities extracted from a particular network, we take the median index across these communities as a measure of their average diversity. The RSD is high for a particular community when classes co-occur in high proportions with other classes with which not many citations are exchanged. RSD is low when classes generally only co-occur in high proportions with other classes with which they exchange many citations. Specifics of the RSD can be found in Section B.2. This kind of analysis, when compared to the network comparison methods above, may be considered relatively myopic. It can only capture the internal composition of individual communities without accounting for the relationships between the pairs of technologies in other communities. However, this calculation may provide insight into the origin of differences we find for the network-level comparisons.

Lastly, we calculate the spread of technologies across the extracted communities. A priori, we do not know what the relationships between the communities are, so we cannot integrate a distance metric to account for the level of surprise that a family assigned a particular class is found in a given pair of communities (as we did for the previous diversity measure). As such, we implement the Herfindahl–Hirschman Index²³²³23Sometimes referred to as the Simpson index. (HHI) (Hirschman, 1945, Simpson, 1949, Herfindahl, 1950, Hirschman, 1964) to measure the extent to which classes are splintered across communities. The details of this calculation can be also found in Section B.2. The HHI is maximised when all families assigned a particular class are in the same community and minimised when there are the same number of these families in each community. Again, the median HHI across all communities is compared across the networks. Like the Rao-Stirling index above, this calculation may add additional colour to the more comprehensive network comparisons. It is important to note that while we believe that it is desirable that communities are able to capture, to some extent, the large-scale structure of the technology-level networks, neither the spread of technologies across communities, nor the internal diversity of communities, is a test of the performance of the community extraction exercise.

It is important to note that the optimal parameters for the community partitions for the three networks are different—the optimal number of communities found for the multilayer network is 15, while for the others it is 7. For this reason, we run the community-detection algorithm for each of the non-optimal partitions (7 for the multilayer network and 15 for the others) to obtain a complete set of networks with which we can make fair comparisons. In sum, we construct six bipartite (community-class) networks which we project onto the class nodes to compare with the co-classification and inter-class citation networks.

The results of this analysis can be found in Table 2. First, we find that the communities in the multilayer network generate class networks that are more similar to the co-classification and inter-class citation networks than those generated by the other two networks. This finding holds for both individual-link-level comparisons (Frobenius) and when higher-order relationships are taken into account (DeltaCon), for both optimal and non-optimal partitions of the multilayer network. Further, we find that the average RSD of the individual communities is lowest, while classes are the most evenly distributed across the communities (low HHI), in the multilayer case.

These observations lend themselves to some interesting interpretations. When looking at all communities, in combination, those extracted from the multilayer network imply technological relationships that are closer to the explicit technology networks than the flattened or single-jurisdiction approaches. However, the diversity calculations suggest that this observation is not simply driven by the extraction of homogeneous communities that group technologies in a straightforward manner. In fact, technology classes are more thinly spread across communities in the multilayer case, while the average internal diversity of classes is generally lowest for this network once known technological similarities between classes are accounted for. This suggests that, on the micro-level, the multilayer (relative to the single-layer) network approach is more sensitive to citation linkages than co-classification, but is nonetheless better able to represent real technological relationships on the meso- and macro-levels.

Indeed, our results are consistent with the conclusion that the multifaceted nature of the technological relationships that are embedded in citation data may be partially lost when a multilayer network is flattened into a single-layer one. This view rests on an assumption that different technology types can be related to each other in different ways. For example, let’s assume that applicants filing a patent assigned to class A prefer to cite families assigned to class B, while examiners examining the same patent prefer to cite those assigned to class C. When, such as in this example, these different relationships are driven by different citing parties, the erasure of citation context will lead to the loss of this nuance. This problem may be exacerbated in the presence of higher-order effects, such as if the above citation behaviour only occurs when a fourth class D is also assigned to the patent application. In contrast, the multilayer network approach ensures these nuances and higher-order relationships remain accessible. The retention of this kind of technologically relevant information, particularly with respect to rare or subtle inter-class relationships, would be consistent with the findings displayed in Table 2.

The main limitations of the empirical analyses conducted in this work are those restrictions we placed on the families we chose to include. As we describe in Section 2.3, these restrictions were put in place for a variety of reasons, including data availability, computational limitations, and a desire to demonstrate our approach in a conservative manner. Little can be done about data availability; however, this only affects our ability to examine citation context in the US case, and only for times earlier than the year 2001. In any case, we suggest that families granted after this time provide a sufficiently large sample for the purposes of this work.

The conservativeness of our approach is introduced with the decision to consider only those families with granted patents at all three triadic offices. This means that all offices had access to the same set of prior art, and had the opportunity to share information among themselves. In turn, this would introduce maximum redundancy between layers, and minimise the additional information that can be added by the inclusion of citation context. It is for this reason that we think of our approach as conservative. Extensions of the restrictive, special-case multilayer framework that we examine here are discussed below in Section 4.2, and highlight the potential of this framework going forward.

Lastly, to reduce the computational complexity of our analyses, we restrict the included families to those classified into CPC class Y02. While we maintain that this subset is an appropriate representation of the patent citation network as a whole, there may be arguments against its generalisability. However, in the case that this class contains a more homogeneous set of families than the set of all families (which is almost certainly true), then the inter-class structure that we are able to explore is likely to be less rich and less nuanced than that of the full network. Detecting higher-order nuances is precisely the domain in which we suggest the multilayer network excels, so following this logic would lead us to conclude that the current approach is, again, a very conservative one.

This work aims to describe the construction of multilayer patent citation networks then conceptually and empirically justify their use. This framework may prove to be of particular interest to those who would prefer representations of technological relationships that are not as sensitive as extant frameworks to the idiosyncrasies of individual patent offices. However, both the layers that are selected to comprise the network and the appropriate empirical methods to extract information from this network will depend on the specific use-case. Here, we describe the myriad methodological doors that are opened with the introduction of patent-based multilayer networks into the broad field of science, technological, and innovation studies.

The obvious extension to the current work is to take a less conservative approach with respect to the subset of families and citations considered. This can take the form of additional layers, nodes, or links. The addition of layers corresponds to the addition of new citation contexts (such as in-text citations (Verluise et al., 2020)) or the addition of new jurisdictions. The addition of nodes and links, on the other hand, would relax the condition that a family be triadic. Citations between triadic families only make up a tiny portion of all citations made and received by these families. For example, in Figure 1, we show the triadic ego network of the family with USPTO equivalent US-6819081-B2. In this restricted network, this family only receives 4 citations from other triadic families classified into class Y02. If we remove all restrictions on the patents we include in our network, however, this family receives almost 50 citations; about 90% of these are from families that have a triadic member, and about 95% are from families that are also classified into Y02. As such, removing the triadic family requirement but keeping the network restricted to the triadic offices and the Y02 classification would dramatically increase the sample size.

Multilayer citation networks can also be flexibly aggregated. Just as one can analyse the inter-class citation network for a single jurisdiction or citation context (e.g., US applicant citations), it is also possible to include additional layers containing the equivalent information for other jurisdictions or contexts. In fact, in the same way that we use families to align layers in the current work, any metadata that connects groups of patents between network layers forms a natural multilayer configuration. Classes, firms, and inventors can all be linked across jurisdictions and citation contexts and their networks analysed in a multilayer framework. Even in the single-jurisdiction US case, for example, the relative positions of firms in the inter-firm citation network will depend on whether one uses examiner citations, applicant citations, third-party citations, or in-text citations. Because firms can be represented as nodes across all of these context-specific networks, multilayer network tools may be applied to obtain a comprehensive and integrative view of the network structure without abandoning citation context. Citations to non-patent literature such as scientific articles is challenging to incorporate into patent citations networks generally, but it is certainly possible to treat this information as family-level metadata — perhaps to construct a bipartite network similarly to how technology classification was used in Section 3.3. More complicated uses of this information could match institution and inventor data from patents onto scientific articles to extend recent work on the multilayered interplay between authorship and the broader dynamics of science and collaboration into the technological domain (Omodei et al., 2017, Nanumyan et al., 2020, Zingg et al., 2020).

In addition to these data extensions, the conceptual arguments against the omission of citation context lead to a strong case for the further application of novel tools designed for the study of multilayered systems. To return to the public transport analogy, it would be unwise to treat all modes of transport as equal if you are trying to find the fastest route between two places in the network. In the same way that the time and financial costs of using different modes affects the route choice between two points in a physical landscape (which will be moderated by the amount of time or money you had), citation networks are embedded in a technological landscape (Kauffman et al., 2000, Fleming and Sorenson, 2001) and different types of citation may traverse this landscape in different ways. This intuition has significant consequences for the analysis of citation networks. For example, any algorithm that ‘walks’ through the network, such as PageRank, should consider the ‘cost’ of each link in a similar way to one plotting a route through a multilayered transportation network. The application of multilayer network methods opens the door to a menagerie of new analytical tools to develop more sophisticated and tailored metrics for studies of technical change and the nature of innovation systems. For example, the identification of patent thickets (Shapiro, 2000, Bessen, 2003) is often conducted through, or supported by, citation network analysis (Von Graevenitz et al., 2011, Zingg and Fischer, 2018, Yuan and Li, 2020). The multilayer framework may assist in these studies — thicket identification depends crucially on the citation context (blocking vs. non-blocking citations) and the jurisdiction (a thicket is necessarily a single-jurisdiction phenomenon). Adding citation context and linking families across jurisdictions for direct comparison may allow for thickets to be more easily distinguished from fields with dense, but non-overlapping, intellectual property rights. For example, when calculating clustering coefficients in multilayer networks, one can specify weights for different kinds of citation or penalise cycles that move between layers (De Domenico et al., 2013). This kind of flexibility can be used to operationalise the definition of thickets in a way that doesn’t simply ignore applicant-provided citations or citations from other jurisdictions, which may not be entirely irrelevant, particularly at the firm level.

Network centrality is another important concept that is generalised in the multilayer case (Solá et al., 2013, Solé-Ribalta et al., 2014, De Domenico et al., 2015, Taylor et al., 2021), and can also be readily applied to citation networks. For example, without citation context, it is hard to know whether firms are central because they block the patents of competitors or are a source of knowledge from which other firms build. Further, firm centrality will likely depend on the jurisdiction one examines, so multilayer centrality may give a more holistic view of their centrality in global markets.

Both technology roadmaps (Lee et al., 2009) and technological trajectories (Verspagen, 2007) may be significantly altered by the incorporation of citation context, as different kinds of citation appear to hold different information, which may, in turn, be useful for forecasting or tracing different kinds of technical change (Acemoglu et al., 2016, Mariani et al., 2019). So-called ‘main paths’ in technological trajectory analysis (Hummon and Dereian, 1989, Verspagen, 2007) could be particularly sensitive to the weights that are placed on, or empirically determined for, different layers or citation contexts. The multilayer framework may also conceptually aid traditional economic analyses (Cai and Li, 2019), for which it is possible, for example, to allow layers to differ in importance when constructing proxy network variables that attempt to capture an abstract concept.

Lastly, pair-wise interactions may not be sufficient to describe the complex behaviour of interactions between the components of innovation systems that are accessible through citation networks. In particular, the interactions between firms or technology types that are visible in citation networks may be better represented through higher-order interactions (Lambiotte et al., 2019, Battiston et al., 2020, 2021). For example, the patenting and citing behaviour of firms may be described at several different scales. Higher-order representations allow us to differentiate changes in citation behaviour of a firm in response to sector-wide changes from the pairwise interactions between a firm and every other firm in its sector. Higher-order interactions can exist within layers of multilayer networks and it is possible that different higher-order behaviours are observable in different patent systems. In any case, it is clear that applications of network frameworks beyond single-layer networks with dyadic links are very much in their infancy in the field of innovation studies, and hold huge potential as more realistic abstractions of innovation systems.

The authors thank the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting Martina Contisciani. MC and CDB were supported by the Cyber Valley Research Fund.