The value of indirect ties in citation networks: SNA analysis with OWA operator weights
Introduction
Work on citation networks has been increasing [58], [6], [48], [62], and the growing interest in different network measures is based on their impact on our understanding of the knowledge diffusion process in disciplines (in the case of academic citation networks) and technological innovation (in the case of patent citation networks). Citation networks have several important features, including showing the relation between number of citations and time. For example, the number of citations received by a node (paper or patent) decreases with age, and the number of citations to a given node is considered a good estimate of its relevance and prestige within the network. Citation networks are directed and essentially acyclical.
We know that knowledge flows from one node to another; thus, the influence of previous nodes on a citation path can be considered important for understanding the importance of citation network nodes. Studies employing social network analysis (SNA) to analyse citation networks usually measure network centrality by considering direct ties [72], [18], [52]. Network centrality measures the number of each node’s connections, and the number of ties is an indication of the importance of the network node [11]. Some studies employ specific algorithms to map citation networks and understand the flows of knowledge across them. However, very few studies investigate more than three generations of citations [74], [70]; examining patent citations over several generations could enrich our understanding of citation network dynamics.
This paper contributes by ranking patent citations using ordered weighted averaging (OWA) [25], with the aim of obtaining a score that explains the longevity of patents over time. This approach provides a better explanation of patent success than SNA alone. The basic idea is that the diffusion process in directed networks is explained better by considering the indirect citations received over time than by relying on purely local measures such as citation counts. Analysis of indirect ties sheds light on otherwise underestimated aspects of citation networks. We show how information and knowledge flow between a network’s nodes.
The proposed OWA operator weights proposed by Emrouznejad and Amin [25], can be used for preference ranking aggregation. In the present study we employ their formulation, assuming a number of patents and the corresponding number of direct and indirect citations, to estimate a score for each patent. These scores should reflect the impact of direct and indirect citations on patent life.
The remainder of the paper is organized as follows. Section 2 discusses the literature on patent citations data. Section 3 focuses on one SNA algorithm, the Hub and Authorities, used for citation network analysis. Section 4 discusses the OWA method and Section 5 describes the data. Section 6 presents the results of application of these SNA algorithms to patent data. Section 7 discusses the results and offers some conclusions. There is also a supplement document that shows details of the results on each node, this document is available on request.
Section snippets
Patent citations
The increase in international patenting activity has resulted in increased use of patent data in research on technological change and innovation, to capture aspects of successful product innovation in firms, and the spread of technologies over time. Patent data are popular because of (a) their availability and (b) their utility as technology indicators [45], [18]. The combination of patent citations and SNA has been employed in several studies to assess the importance, radicalness and novelty
SNA algorithms: background
A popular approach in SNA is citation network analysis to ‘weight’ the importance of individual patents (or journal articles) by counting the number of citations received [41]. Patent citations are used to proxy for knowledge flows across a technological field, and for their significance. Patent citation network analysis has been used to trace the development of technological domains and to assess the importance of a patent in a discipline [7], [30], [8], [27].
In the case of patent data, patent
Centrality measures
Two SNA measures are widely used in analysing citation networks, in-degree and out-degree centrality. The former indicates the number of incoming ties, that is the number of direct citations received by a node in a citations network. The latter refers to the number of outgoing ties and indicates how easily a node can reach other nodes. For example in the citations network depicted in Fig. 2. the degree centrality of Node A is 3.00, and the out-degree is 0.
A third measure, closeness centrality,
Ordered weighted average operator (OWA)
The family of OWA operators proposed by Yager [75] includes cumulative operators for membership aggregation. Following this conceptualization, the OWA weighting vector was proposed to introduce the decision maker’s attitude [76], and the OWA operator has been applied in various disciplinary contexts such as decision making under uncertainty [78], fuzzy information retrieval system [47], [39], e-commerce performance evaluation [40] and data mining [68]. Emrouznejad and Marra [26] provided a
European Patent Office (EPO): Data source
Our data source is the EPO Worldwide Patent Statistical Database (PATSTAT), which includes patents from 81 national and international patent offices, detailed information on patents published in the EU, and citations from EPO to non-EPO patents, that is, backward and forward citations to other world patents. We identify our patents based on the six categories in the International Patent Classification (IPC) related to the renewable energy sector (wind, solar, geothermal, ocean, biomass, waste),
Results and discussions
We ran the analysis for each patent. Hubs and authorities weights and detailed results for all eight patents are available on request but to avoid repetition in this section let us focus on Patent 2 (P2) and its network (hereafter NP2) only. Results of the OWA scores are described in the last section.
An application of the proposed OWA weights in preference ranking
Consider the following example to illustrate the weights generated by the OWA operator. There are eight patents, i = 1,…,8 and j = 1,…,9, the numbers of direct and indirect citations are listed in Table 9.
Assume and let’s use OWA measure presented in Model 3, hence we have:Empty Cell 0.28 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02
And the results ranking the eight patents are given in Table 10.
The decision to set is to attribute more importance to citations received in a
Conclusions
This study analysed patent citations networks in the specific field of renewable energy, based on patents retrieved from the EPO database and published between 2000 and 2013. We applied Hubs and Authorities algorithm to identify the most important contributions.
We have argued that the evolution of knowledge within a citations network should consider both direct and indirect citations. SNA underestimates the role of indirect citations and is not able to provide a network measure for them in
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