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Network Maps of Technology Fields: How Measures of Relatedness Influence Network Structures

The structure of the total technology space, together with the specialized knowledge positions of the inventors, companies and countries, conditions the prospect of their next innovations. Prior studies have proposed representing the technology space as a network of patent technology classes connected by links weighted according to their relatedness. Although the choice of relatedness measures affects the structure of the resulting networks, such measures have not been assessed in terms of their influences on network structures. In this paper, we first present six measures based on the similarity of knowledge bases of different technology fields and, alternatively, on the likelihood for inventors, organizations or countries to diversify across technology fields. Then, we compare the resulting networks in terms of network structures, vertex and edge properties and their predictability on the importance of the represented technology fields. Based on USPTO patent data from 1976 to 2010 and International Patent Classification, our results suggest that the technology space is almost fully but heterogeneously connected, with extremely weak relatedness between most pairs of technology classes, that is consistent in different types of networks. Our results also suggest that networks using co-reference and inventor diversification likelihood to relate technology fields are strongly correlated with each other, are relatively more correlated with other types of networks, and provide the strongest correlations between network centrality measures of the vertices and the importance of the represented technology fields. These two types of technology networks may be most useful for general network analysis on how the structure of the technology space conditions the search for inventions of different agents.


Introduction
Innovation is a process of searching through different technology fields in the technology space. Individual inventors, technology companies or R&D organizations, and regions and countries continually diversify, i.e., move into new technology fields, or exit from past fields in the space of various technologies. In turn, the structure of the technology space, together with the knowledge positions of innovation agents (e.g., inventors, companies or countries), may condition their trajectories of search for innovation. To assess the knowledge positions and the change in such positions of innovation agents in the technology space, several recent studies have proposed representing and analyzing the technology space as a network of technology fields based on mining patent data (Leydesdorff et al., 2014) and overlaying the patenting activities of individual organizations on the total network map (Kay et al., 2014). Such analysis can potentially help assess knowledge positions of companies or regions and support decision-making on the search for innovation and related capability-building efforts.
In such networks, a vertex represents a technology field and is operationalized as a patent technology class.
The edge between a pair of vertices represents the degree of relatedness between the vertex-represented technology fields and is often measured for knowledge proximity or similarity using patent citation and coclassification data (Breschi et al., 2003;Ejermo, 2005;Engelsman and van Raan, 1994;Kogler et al., 2013).
Such patent technology class networks have been used to assess the diversification of firms across technology fields (Breschi et al., 2003;Jaffe and Trajtenberg, 2002), the change in the respective knowledge space of cities and regions (Kogler et al., 2013), and the movements of their knowledge positions across technology fields in the total space, i.e., entering new fields and/or exiting from prior fields (Boschma et al., 2014;Rigby, 2013).
The results and insights from such network analyses rely on the structures and properties of the constructed network maps. In turn, a patent class network qualified to represent the technology space that requires an appropriate measure of relatedness between technology fields (Joo and Kim, 2010). In other words, the choice of the measure of relatedness between technology fields determines the structure of the network and the insights to be drawn from the network analysis. In the literature, although various relatedness measures have been proposed from different angles or perspectives (Breschi et al., 2003;Joo and Kim, 2010), they have not been systematically compared, assessed and justified for selection for specific applications, primarily due to the lack of consistent criteria or methodology of comparison. As a result, the studies of technology diversification or knowledge position movements of firms, cities and regions in the technology space often simply chose a single measure of relatedness for their strategic analyses, without any comparison of measures to justify the choice.
Considering that the purpose of creating a network representation of the technology space is to use it to study how the structure of the space may affect the positions and movements of innovation agents, the structure of such networks needs to be the main concern when we create and evaluate them. Clearly, the choice of relatedness measures affects the structure of the constructed networks. However, network structures have not yet been used as the lens of comparison and assessment of alternative relatedness measures for constructing patent technology class networks. New measures were often proposed based on qualitative justifications motivated by certain rationales. Herein, we propose to quantitatively assess and compare alternative relatedness measures in terms of their influences on the structures of the resulting networks. The field of complex network analysis has provided a rich set of graph theoretic metrics and visualization techniques to capture and characterize different aspects of network structure patterns. In this paper, we apply some of those to assess and compare the structural patterns of the patent class networks resulting from alternative choices of relatedness measures.
We specifically chose to analyze the relatedness measures that relate the inputs into and the outcome from the design process (or design activities), which yield inventions and patents. Despite the variety of relatedness measures in the literature, the perspective centered on design process has not yet been used to formulate relatedness measures. Specifically, we formulate the first group of three measures to focus on the similarity of knowledge inputs to inventions (indicated by patents) in different technology fields, using patent citation data, and the other group of three measures to focus on the likelihood of diversification of inventors, organizations and countries across pairs of technology fields as the outcome of their design process using patent bibliographic information. The similarity of knowledge inputs to the design processes in a pair of technology fields should condition the likelihood for innovation agents to diversify their innovative activities from one field to the other, suggesting a strong correlation between the networks constructed using these two groups (or types) of relatedness measures. This correlation is useful for the assessment and selection of alternative measures.
USPTO patent data from 1976 to 2010 and International Patent Classification are used to operationalize these alternative measures of relatedness (as weights of the edges) between technology fields (as vertices) and construct the network representation of the technology space. The resulting networks are assessed and compared in terms of network structure patterns, vertex and edge properties and their predictability on the importance of the represented technology fields. The results suggest one superior relatedness measure from each of the two groups, as the networks resulting from them are the most strongly correlated pair, reflecting the strong correlation between knowledge input similarity of technology fields and the likelihood for innovation agents to diversify across them. Networks resulting from them are relatively more correlated with other types of networks and also provide the best predictability on the importance of technology classes according to their network properties. In addition, our network analyses also reveal a few consistent network structure patterns regardless of the choices of relatedness measures used to construct the networks (see Section 5).
In sum, the contributions of this paper are three-fold: (1) A network analysis methodology for comparing, assessing and selecting relatedness measures for patent technology network construction; (2) The identification of good relatedness measures based on our methodology and a design process perspective; (3) The identification of several consistent structure properties of the technology space, regardless of the choices of relatedness measures and resulting networks.
The paper is organized as follows. Section 2 reviews various measures of relatedness of technology fields proposed in prior studies. Section 3 introduces our data, the two groups of relatedness measures, and the network analysis techniques. Section 4 reports empirical results and discusses main findings. Section 5 concludes the paper.

Measures of relatedness between technology fields
Creating the network of patent technology classes to represent the technology space requires a measure of the "relatedness" between pairs of technology classes. A qualified measure should capture the degree of ease with which the knowledge and skills required to invent technologies in one class can also be used to invent technologies in the other class. Such a degree can be indicated by measures of knowledge proximity or similarity of different technology fields, or measures of the likelihood for innovation agents to invent technologies in different technology classes. Herein, we review various relatedness measures in the literature.

Patent citation-based measures of relatedness
One strand of the measures uses patent citations to calculate indicators of knowledge similarity of technology fields. For instance, to create the technology map of IPC classes, Leydesdorff et al. (2014) used the cosine similarity index to normalize the citing-to-cited relationships between technology classes in the aggregated citation matrix. The angular cosine value of the two vectors of citations from two classes to other classes captures the knowledge similarity of their knowledge bases as represented by patent citations. The cosine measure of similarity between two variable vectors is better than the Pearson correlation coefficient when there are large numbers of zeros (Ahlgren et al., 2003). Kay et al. (2014) also used the same cosine similarity metric to calculate the "technology distance" among different citing patent categories, but some of their categories combine original IPC patent classes to optimize the size distribution of classes for the sake of visualization.
Indeed, Jaffe (1986) was the first to propose the cosine index, but he used it measure the correlation between a number of vectors representing the distribution of firms' patents over a set of fields.
In addition, in the analysis of relatedness between patents, co-citations, i.e., the number of shared forward citations of two patents, and bibliographic coupling, i.e., the number of shared backward citations (i.e. references) of two patents, were used to measure the knowledge relatedness between pairs of patents (Iwan von Wartburg et al., 2005;Leydesdorff and Vaughan, 2006). Such a co-citation index can be further normalized over the total number of citations for each article, i.e., the Jaccard Index (Small, 1973), or over a probabilistic measure of expected co-citation counts (Zitt et al., 2000). The formulations of co-citations or bibliographic coupling of patents or academic articles can be migrated to the process of measuring the relatedness of different technology classes.

Patent classification-based measures
Scholars have also used the co-classification information of patents to develop indicators of knowledge proximity between technology classes. A patent belongs to at least one, but usually multiple, classes, assigned by the patent examiners of the issuing offices. The relatedness between technology fields can be measured according to the co-occurrence of classification codes assigned to individual patent documents (Engelsman and van Raan, 1994). The assumption is that the frequency in which two classes are jointly assigned to the same patent signals the knowledge relatedness of the classes, in terms of knowledge links and spillovers. Jaffe (1986) was also the first to apply the cosine index to analysis of the proximity of firms' technological portfolios based on the symmetrical matrix of the frequency of two technology classes being jointly assigned to the same patent that belongs to the observed firms. Later, this cosine index was adopted for the general symmetrical co-occurrence matrix in which each cell represents the total number of patents that are assigned with both technological fields represented by the respective row and column, to measure the relatedness between pairs of technology classes (Breschi et al., 2003;Ejermo, 2005;Engelsman and van Raan, 1994;Kogler et al., 2013). Furthermore, Nesta and Dibiaggio (2005), using the same co-occurrence matrix, measured the relatedness between technology fields as the deviation of observed overlap patents between technological classes from the expected overlap patents, following Teece et al. (1994) who measured the relatedness between industrial fields. Leydesdorff and Vaughan (2006) argued that the symmetrical co-occurrence matrix contains similarity data and can be analyzed directly, whereas further normalization of the co-occurrence matrix using the Pearson correlation or cosine may distort the data and generate spurious correlations. Leydesdorff (2008) further proposed analyzing the asymmetrical classification assignment matrix, with patents as the units of analysis and the technology classes as the column variables, and normalizing the column variables using the cosine to create the network of technology classes. He also found that networks built using classification data match poorly with those generated by citation data, and the classification data might be less useful than co-citation data for technology network mapping, primarily because the classifications were assigned poorly by the ISI staff. In addition, Joo and Kim (2010) also argued that co-classification measures may not directly assess the relatedness among technological fields and proposed to create a multi-dimensional contingency table to represent patent classification data and apply the Mantel-Haenszel common odds ratio on the table to measure the relatedness among technology fields.

Likelihood of diversification as measures of relatedness
Another group of measures utilizes the data on the diversification behaviors of innovation agents (e.g., countries, regions, cities, organizations or inventors) to measure the relatedness between technology fields. In their study of the product space, Hidalgo et al. (2007) measured the proximity between two product categories as the likelihood for an average country to develop strong relative comparative advantage (RCA) in one product category given that it has developed strong RCA in the other. The assumption is that this likelihood is high if the capabilities required to produce products in one category are similar to those required to produce another product. In other words, the likelihood for the diversification of countries across two product categories may be a measure of the similarity of the knowledge base of these two product categories. Boschma et al. (2013) applied this product relatedness measure to studying the emergences of new industries in Spain. Although these studies of the product space can be used for export and import data and the custom classifications of products, a similar measure can be applied to patent data and technology classes to approximate the relatedness of technology fields. In fact, a mathematically similar index called the Revealed Technological Advantage (RTA) has been used to measure the pattern of technological specialization of innovation agents (Cantwell and Vertova, 2004;Hall et al., 2001). Boschma et al. (2014) further applied it to calculating the likelihood of technology diversification at region and city levels as weights on the edges in the network of patent technology classes.
Despite the variety of relatedness measures developed based on different perspectives and using different data items of patent documents, these measures have not been assessed and compared using a consistent methodology and criteria. In this paper, we present a framework to compare alternative relatedness measures by comparing the structures of the networks based on them. In demonstrating our approach, we adopt several relatedness measures based on the co-reference, cosine similarity and diversification likelihood and analyze the technology network structures resulting from them. In particular, drawing on the authors' earlier experience and research on the design process, we consider the citation-based relatedness measures as indicators of the similarity of knowledge inputs into the design process and the diversification likelihood-based relatedness measures as results from the design process, which yield inventions and patents. Following that innovation agents are more likely to diversify across technology fields with similar knowledge bases, there should be a strong correlation between the networks built on the input-based and outcome-based relatedness measures. This correlation is useful for the assessment and selection of alternative measures.

Data
In this study, we construct and compare networks of patent technology classes using different relatedness measures. Specifically, the vertices in our networks are technology classes defined in the International Patent Classification (IPC) system, following many other authors who have considered IPC classes the most suitable and stable representations of technology fields (Leydesdorff et al., 2014). The IPC system includes 8 broad technical domains, which can be subdivided into, for example, 3-digit and 4-digit level subclasses. For the best visualization without losing necessary details and resolution of the technology landscape, we chose 3-digit classes to represent vertices in networks. Some undefined classes, for example, "A99 -subject matter not otherwise provided for in this section," are excluded from the analysis. As a result, our networks all contain 121 vertices, i.e., 3-digit level IPC classes, containing 3,911,054 utility patents in 1976-2010 from USPTO. Our data set only excluded 26 utility patents that have an invalid or null IPC classification code out of the total USPTO database for the analyzed period of time. For our analysis of the invention agents, we used the unique assignee identifiers created by the National Bureau of Economics Research (NBER) (Hall et al., 2001) and the unique inventor identifiers created by the Institute for Quantitative Social Science at Harvard University (Li et al., 2014) Relatedness measures The edges between classes are weighted according to the degree of relatedness between pairs of technology classes. A qualified measure of the "relatedness" should be able to capture the intuition that the technical knowledge and capability required to invent technologies in one technology class can also be used for inventing technologies in the other class. This intuition can be operationalized by empirically measuring the following: (1) the similarity of knowledge inputs required by the design activities in different technology fields, using patent citation data, or; (2) the likelihood for the same invention agent to have strong design capabilities and invention records in different technology classes, using the patenting behavior data of the agents.
Knowledge inputs to design activities should condition the resulting activities of invention agents, implying the correlations between networks built on the measures following both (1) and (2) rationales. There might be many measures that qualify for modeling the knowledge input similarity and the likelihood for agents to diversify across different fields. In this study, we chose three representative measures in each of the two categories to construct technology networks and compare them. Table 1 summarizes these measures. In the next section, we introduce how to calculate these measures using patent data.  A1. "Co-Reference": the ratio of the shared references to all unique references of patents in a pair of classes, formulated as where C i and C j are the numbers of backward citations (i.e., references) of patents in technology classes i and j.  (Jaccard, 1901). This measure may have a bias for estimating the relatedness between a technology class that has a large number of reference counts and another class that has a low number of reference counts.
A2. "Class-to-Class Cosine Similarity": the cosine of the angle of the two vectors representing two technology classes' distributions of citations into all patent classes (Leydesdorff, 2007), formulated as where C ij denotes the number of citations referred from patents in technology class i to the patents in technology class j. The cosine value is between [0,1] and indicates the similarity of the knowledge bases of the inventions in two technology fields.
A3. "Class-to-Patent Cosine Similarity": the cosine of the angle of the two vectors representing two technology classes' distributions of citations into specific unique patents instead of aggregated classes. The same formulation as (2) applies, but C ij now denotes the number of citations of all patents in class i to the specific patent j. Measure A3 has a better resolution than measure A2, whereas computation is slightly more complex.
The next three relatedness measures (B1, B2 and B3) use the data related to the innovation agents and the classifications of their patents, i.e., the output from design process, to measure the likelihood that innovation agents can diversify by leveraging knowledge in one technology field for invention in the other field.
B1. "Inventor Diversification Likelihood": minimum of the pairwise conditional probabilities (R i,j ) of an inventor having strong inventing records in one class, given that he/she also has strong inventing records in the where RTA c,i denotes inventor c's revealed technological advantage in technology class i RTA c,i is an indicator of the relative inventive capacity of inventor c in class i. RTA c,i >1 means agent c has more patents in class i as a share of his total patents than an "average" agent; otherwise, if RTA c,i ≤1 . This measure is adapted from several recent studies (Boschma et al., 2014;Cantwell and Vertova, 2004;Hidalgo et al., 2007).
In the context of patent technology classes, a high R i,j value indicates a higher likelihood for an inventor to leverage solutions or knowledge across technology fields i and j or to diversify his/her inventive activities across fields i and j. It may further indicate the similarity of technical knowledge or capabilities required for inventions in fields i and j.
Using the inventor level data, it is possible for RTA to be infinite. Therefore, Cantwell and Vertova (2004) proposed normalizing the RTA values to the range between 0 and 2. To calculate this measure using information about the patenting records of specific inventors, we use the unique inventor identifiers from the Institute for Quantitative Social Science at Harvard University (Li et al., 2014).
B2. "Organization Diversification Likelihood": the formulation is the same as the "Inventor Diversification Likelihood" above (Eq. 3 and Eq. 4), except that the agent is now an "organization", which is often a "company", university, or public R&D agency.
B3. "Country Diversification Likelihood": the formulation is the same as the "Inventor Diversification Likelihood" above (Eq. 3 and Eq. 4), except that the agent is now a country. Any measurement can be conducted for cities, provinces, or a larger region, such as Southern Eastern Asia, Asia Pacific.
Then, networks are constructed based on these six relatedness measures in two groups, using USPTO patent data and IPC classes. With these networks, we investigate network statistics at the edge and vertex levels and the overall network structure levels.

Network comparison: metrics and visualization
We utilize some of the visualization techniques and graph theoretic metrics from the field of complex network analysis to capture and characterize different aspects of network structure patterns of the patent class networks resulting from certain choices of measures of relatedness. The purposes of the network comparison analysis are two-fold: (1) revealing how the choices of relatedness measure may result in different network structures and suggesting good measures and related networks; and (2) identifying consistent network structure patterns regardless of the choices of relatedness measures used to construct the networks.
Because the networks are almost fully connected, we use two techniques to visualize the networks that shed the edges and exhibit the main structure. One is to remove the edges one-by-one, starting from the weakest one, until one additional edge removal would disjoint the total network. The other method is to visualize the maximum spanning tree abstracted from the full network structure of the network. The maximum spanning tree for a network only keeps those strongest edges that minimally connect the network into a tree. In addition, we also examine adjacency matrix representations (in which each off-diagonal cell denotes the technological relatedness between pairs of technological fields corresponding to the row and column) to reveal the overall structure patterns of full networks.
For quantitative assessments, we compare the networks in terms of the distributions of edges by weights (i.e., relatedness values) and vertex centralities. In social, technological and general network analysis, various network centrality metrics have been developed and used to identify and compare the relative importance of different vertices in a network (Newman, 2010). These centrality measures provide means to investigate and compare the structures of different networks with the same set of vertices but different weights of edges or topologies connecting them. For instance, the same vertices (representing specific technology fields) can be more important in one type of network than in another given their higher centralities (determined by measures of relatedness among technology fields) in one network than in the other. The following vertex centrality measures are applicable for weighted networks (Newman, 2005) and used in our analysis: (1) Degree centrality: the sum of the weights of the edges connected to the focal vertex; (2) Eigenvector centrality: the value of the respective element (for the focal vertex) of the Perron eigenvector of the adjacency matrix; (3) Clustering coefficient: the geometric average of the edge weights of the sub-network; (4) Random walk betweenness centrality: the counts of paths based on random walks between pairs of vertices that pass through a given vertex. Furthermore, we also compare the degrees to which vertex centralities can predict the importance of different classes measured by their total forward citation counts, i.e., the citations received from later patents in different networks. In the technology space, some fields are more important than others. Also, the centralities (i.e., network positional importance) of technology classes in the entire network may result in or result from the actually importance of the technology classes in terms of size and value to future inventions. We operationalize this intuition by investigating in which of the six networks the centrality measures of vertices are strongly correlated with the actual importance of the represented technology fields, as measured by both (1) the total patent count and (2) the total count of forward citations of the patents in a field. Forward citation count of a patent has been found to be an effective indicator of the economic value of a patent in a number of prior studies (Albert et al., 1991;Hall et al., 2005;Harhoff et al., 1999;Lee et al., 2007;Trajtenberg, 1990).
In the next section, we present the network visualization and comparison analysis using the methodology and data introduced in the previous section.

Results and Discussion
Before we compare different networks, we examined the changes in each of them over time. Table 2 (Hinze et al., 1997) that also showed that technology networks are stable over time. For the best empirical estimation of the relatedness between technology fields, we used the networks constructed using the patent data in the entire time period from 1976 to 2010 for our comparative analyses.
Furthermore, the network using inventor diversification likelihood to measure edge weight appears to be visually similar to the three networks based on measures of knowledge base similarity, in terms of both network structure ( Fig. 4 in matrix form) and edge weight distribution (Fig. 5). To investigate this aspect in further detail, we calculate various coefficients of correlations of these networks. Table 3 reports the Pearson correlation coefficients between the weights (i.e., relatedness values) of respective pairs of edges in different networks. There are a few noteworthy findings. First, in the first group of three measures (A1, A2, A3) focusing on knowledge base similarity, the co-reference (A1) network is consistently the most correlated one with the three networks in the second group (B1, B2, B3) focusing on the diversification likelihoods. The network using A2 "class-to-class cosine similarity" is the least correlated one in the first group.

Correlation of edge weights between different networks
In the second group of three measures (B1, B2, B3), the network using "inventor diversification likelihood" (B1) to measure edge weights is consistently the most correlated one with the three networks in the first group (A1, A2, A3), whereas the network using "country diversification likelihood" (B3) is the least correlated with other networks.
Among all network pairs, the strongest edge weight correlation (i.e., 0.914) exists between these two networks using co-reference (A1) and inventor diversification likelihood (B1) to measure inter-class relatedness. This strong correlation may be because the knowledge relatedness of two technology fields largely determines the ease for individual inventors to diversify their inventive activities across them. This determining effect is lesser for organizations, which aggregate many individual inventors, and even lesser for countries, which aggregate many organizations.

Correlation of vertex centralities between different networks
In this research, we calculate four centrality metrics (including degree centrality, eigenvector centrality, weighted clustering coefficient and random walk betweenness) for each of the 121 vertices in each of the six technology networks and then use Spearman's rank correlation coefficient to measure the similarity (or differences) between them. The purpose is to discover whether and how the relative network positional importance (in terms of centralities) of the same set of 121 vertices (i.e., technology fields) may differ across network types due to the choices of relatedness measures used to construct the networks. Table 4 reports the correlation coefficients. In all cases (using four different centrality metrics), the co-reference (A1) gives the most correlated network with other networks; the inventor diversification likelihood (B1) network comes second (and is the most correlated one from the second group). Again, the country diversification likelihood (B3) network is the least correlated one.
Correlation of vertex centralities and importance of technology fields in different networks As discussed in Section 3.3 on methodologies, the network centralities (i.e., positional importance) of technology classes in the space may be related to the actual importance of the represented technology fields in terms of size (measured as the total number of patents) and value for future inventions (measured as future citation counts). Therefore, we compared the degrees to which vertex centralities can predict the importance of different classes measured by their total forward citation counts, i.e., the citations received from later patents in different networks. In the technology space, some fields are more important than others. Additionally, the network centralities of the technology classes in the space may result in or result from the actually importance of the classes in terms of size and generating knowledge spillover effects to affect general technology changes.
Therefore, we calculated Spearman's rank correlation coefficients between total patent counts and total forward citation counts of the 121 technology classes (from 1976 to 2010) and the network centralities of the vertices representing them in these six different networks. Table 5 reports the results, which reveal several consistent patterns across scenarios.
First, vertex centrality is consistently more correlated with forward citation counts than with total patent counts of the technology classes in all combinations of network types and centrality measures. Second, among all six networks, the co-reference network (A1) gives the highest correlations between different centrality measures and both total forward citation counts and total patent counts. The inventor diversification likelihood network (B1) gives the second highest correlations in this regard. Third, for the co-reference and inventor diversification likelihood networks, eigenvector and degree centralities are more predictive on both total patent counts and forward citation counts of technology classes than the other centrality measures. These results suggest the choices of centrality measures and networks for use in general technology network analysis for insights related to technology changes.

Conclusion
In this study, we have presented a network analysis methodology for comparing, assessing and selecting relatedness measures in terms of their influences on the structures of resulting technology networks. This methodology is demonstrated via an analysis comparing the structures of networks built on six different measures of inter-class relatedness. These measures of comparison were chosen and grouped based on a design process perspective, addressing the inputs to and outcome from the design process. Our comparative analysis suggests that two relatedness measures, co-reference and inventor diversification likelihood, are relatively better choices for constructing technology networks following the design process perspective.
Our results also reveal several consistent structure properties of the technology space, regardless of the choices of relatedness measures, including the following: (1) All technology networks are almost fully connected, meaning that any pair of technology classes is related to each other to a certain degree.
(2) In all networks (except the country diversification likelihood network), the majority of edges are extremely weak, meaning that the technology space is sparse.
(3) Vertex centrality is consistently more correlated with forward citation counts than with total patent counts of the technology classes in all combinations of relatedness measures and centrality measures.
(4) Eigenvector and degree centralities provide good prediction of the actual importance of technology classes (indicated by their forward citations and total number of patents in the classes) across different types of networks.
Moving forward, one area of future work is to apply additional analytical lens, e.g., clustering or community structure, to assess the structure of technology networks. One question to ask is whether and how the choices of relatedness measures may affect the structures of communities of technology fields. It will also be interesting to assess additional relatedness measures proposed in the prior literature in terms of how they affect the structures of the resulting networks. In addition, better visualization techniques may further improve the analysis of patent technology networks.