Eigenfactor

The Eigenfactor is a journal metric, which was developed by Bergstrom and his colleagues at the University of Washington. They invented the Eigenfactor as a response to the criticism against the use of simple citation counts. The Eigenfactor makes use of the network structure of citations, i.e. citations between journals, and establishes the importance, influence or impact of a journal based on its location in a network of journals. The importance is defined based on the number of citations between journals. As such, the Eigenfactor algorithm is based on Eigenvector centrality. While journal-based metrics have been criticized, the Eigenfactor has also been suggested as an alternative in the widely used San Francisco Declaration on Research Assessment (DORA).


Introduction
This chapter provides an overviewonthe Eigenfactor™,ajournalmetric,which was developedb yB ergstrom (2007) and his colleagues at the Universityo fW ashington.They invented the Eigenfactor as aresponse to the criticism against the use of simple citation counts (Bergstrom, 2007).They alsoc laimed an eed for alternative metrics (West,B ergstrom and Bergstrom, 2010), which in this cases hould not be confused with altmetrics,w hich are metrics to track mentions of scholarlya rticles online (Priem et al., 2010).
The Eigenfactormakesuse of the network structure of citations, i. e. citations between journals (Bergstrom,2 007).The citations are retrieved from JournalC itation Reports (JCR), which is ap art of ClarivateA nalytics' Webo fS cience (West,B ergstrom, and Bergstrom, 2010).The Eigenfactorisdefined as aflow-based journal ranking,b ecause it simulates the workflow of ar esearcher searchingt hrough journals using citation links (Bohlin et al., 2016).By doing so, it is "interpreted as ap roxy for how oftenaresearcher who randomlyn avigates the citation landscape accesses content from the journal" (Bohlin et al., 2016).These navigational traces,i .e.c itations between journals, can be used to calculate ajournal'sinfluence ( Chang,McAl-eer,a nd Oxley,2 013), importance of aj ournal to the scientific community (Bergstrom, West,a nd Wiseman, 2008) or even impact of aj ournal ( Ball, 2017), in which "importantj ournals are those thata re highlyc ited by important journals" (Bohlin et al., 2016).The Eigenfactora lgorithm (West,B ergstrom, and Bergstrom, 2010) is based on Eigenvector centrality, which is ac ommonlyu sed measure to calculate centrality in network analyses (Martin, Zhang,a nd Newman, 2014).Bergstrom (2007) describes the approach of ranking journals as similar to the wayG oogle'sP ageRank algorithm works.Google ranks websites based on the number of hyperlinksbetween different websites, but all hyperlinksare not considered as equal, as ah yperlink from aw ebsitet hat alreadyr eceivesasignificant number of links is more valuable than ah yperlink from awebsitewith onlyafew links.The Eigenfactorr anks journals in as imilar manner by using citations between journals.Bergstrom describes the approach as follows: "We measure the importance of acitation by the influenceo ft he citing journal divided by the totaln umber of citations appearingi nt hat journal" (Bergstrom, 2007).Bergstrom also argues thatt his approach corrects the differences between journals and disciplines.That is to say, the "Eigenfactor measures the total influenceofajournalonthe scholarlyliterature or,comparably,the total value provided by all of the articles published in thatj ournal in ayear" (Bergstrom, 2007).Furthermore, Bergstromdeveloped an article influence rank which "is proportional to the Eigenfactor divided by the number of articles" (Bergstrom, 2007).Thisr ank is comparable to the JournalI mpact Factor (Bergstrom, West,a nd Wiseman, 2008).Bergstrom (2007) also proposed aw ay to measure research impact outside the scientificc ommunity.T his was proposed to be done by calculating references to scholarlya rticles from ac urated list of major newspapers, such as New York Times, TheGuardian, Wall Street Journal, Washington Post, London Times, MiamiHerald, Financial Times, Le Monde, Boston Globe,a nd Los Angeles Times.

Role of the Eigenfactor within the Scientific Community
Scientific journals have been an important communication channel for scientific discoveries (Gingras, 2016), ever since the first scientific journalwas established in 1665 (Mack, 2015).While there are differencesb etween academic disciplines, such as the social sciences and humanities that have as trongert radition in publishing books (Hicks, 2005), journals can be found across the rangeo fs cientific research.With the introduction of the Internet and the World Wide Web, the importance of scientific journals as acommunication and distribution channelhas diminished.However,the scientificjournalasapublication venue has not changed much since its earliest beginnings (Auer et al., 2018;Wouters et al., 2019).Auer et al. (2018), for example, highlight that journal publications which are mainlybased on PDFscould be changed to an interoperable format.Thiscould be done by providingthe text in XML(Structured Markup Language).By doing so, the text would provide an improved machine read-ability and linkage between different documents.Thefinal goal with this movecould be to interlink this content in ac omprehensive knowledge graph.Further initiatives explore the possibilityt od ecentralize the journal publication system by applying blockchain technology (Blocher,S adeghi,and Sandner,2 019).
Citations have for along time been considered as recognition of the value of earlier work, i. e. that researchers acknowledge that they have used or found value in the works that they reference.With that,citations have become part of the academic reward system, with highlycited researchers considered to have made agreater impact (Merton, 1973).Citations take, however,along time to accumulate, as the scientific publishing process can take years.To counter this time delay, journal-based metrics have been developed (Fersht,2009).The assumption with journal-based impact metrics is that "better" journals have amore rigorous peerr eview process and that only the "best" research will be published in them.With that,inwhich journals researchers publish is sometimesevenseen as aquality indicator of their work (Chang,McAleer,a nd Oxley,2 013), which in turn mayh avec onsequences on their academic careers (Bohlin et al., 2016;B rembs, Button, and Munafo `,2 013) or even generate questionable financial rewards (Quan, Chen, and Shu, 2017).Furthermore, national journal rankingsa re developed in several countries (Quan, Chen, and Shu, 2017;Huang,2 019).Journal based metrics, such as the Journal Impact Factor,m ay also be heavilyi nfluenced by asmall number of articles that receive the majority of citations (Seglen, 1992).L arivie ´re and Sugimoto (2018), for instance, provided an extensive review of the critique on JournalImpact Factors.Rankingsofjournals are, thus, ah ighly-debated topic because they might alsoa ffect research assessments (Tüselmann, Sinkovics,a nd Pishchulov,2 015).On the one hand, journalr ankingsa re oftentimes alsoaccepted by researchers as part of the publishing process (Brembs,Button, and Munafo `,2 013), while on the other hand, it has been argued that journals with ah igher impact factor seem to be more likelyt op ublish fraudulent work than low-ranked journals (Brembs, Button, and Munafo `,2013;F ang and Casadevall, 2011).Metrics wered eveloped to classify and understand the journal system better (Garfield, 1972),a nd journal metrics have been developedi ns everal contexts.Furthermore, journal-basedm etrics can provide ad eeper insight into the similarityo f journals (D' Souza and Smalheiser,2014).The first study that tried to develop objective criteria on journals based on citation counts was published in 1927,and focused on the main U.S. chemistry journals for the year 1926.The authors concluded that the majority of journals receive ar elativelyl ow number of citations (Gingras, 2016).
As brieflymentioned above, the Eigenfactorwas developed as part of aresearch project at the University of Washington, and the concept is available on apublic website.Bergstrom and colleagues tried to servet he needso fv arious stakeholders, among others the library community,f or example, to support librarians' decisionmaking on journal subscriptions ( Kurtz, 2011).One of the goals of the Eigenfactor is to help academicl ibrarians identify the most important journals when deciding which journals to subscribe to.With the constantlyi ncreasings ubscriptionp rices it is important to know which journals are the most importanta nd that will be used by scholars.Thisalsorelates to the fact that with an ever increasingamount of journals (Bohlin et al., 2016;van Gerestein, 2015) acomprehensive overview without rankingsa nd metrics seems impossible.Even if the quality of aj ournal can onlyb e assessed objectively by human readingo ft he published articles (Bergstrom,W est, and Wiseman, 2008), rankingsa nd metrics to classifyj ournals are ac ommon practice (Bohlin et al., 2016).
Compared to otherj ournal-based metrics, the Eigenfactor has been proposed as an alternative by the San Francisco Declaration on ResearchA ssessment (DORA) (Cagan, 2013).In turn, the Eigenfactor also supports the Initiative for Open Citations (I4OC).The exactextent to which the Eigenfactorisused in the scientific community and research evaluations is unknown.Nevertheless,s tudies on hiring and tenure promotion provide ag limpse into the use of metrics.Alperin et al. (2018), for example, concluded thatmetrics, such as the JournalImpact Factor,are used as ameasure by hiring and promotion committees in Canada and the United States.The Journal Impact Factor,for example, is used in several decision-making processes in national research systems (Bohlin et al., 2016), and instead of evaluatingj ournals it is also used to evaluater esearchers, which is ah ighlyc ontroversialt opic (Fersht,2 009;West,B ergstrom, and Bergstrom, 2010;W outers et al., 2019).

Critical Perspectives on Journal-based Metrics and Comparison to the Impact Factor
While the Eigenfactor provides some advantagest hat have been described above, just like anyindicator,itdoes not come without limitations.The JournalImpact Factor was first described in 1972, and is one of the most common journalrankings (Bohlin et al., 2016;Gue ´don, 2019).It is defined as follows: "The impact factor of ajournal in ag iven year measures the averagen umber of citations to recent articles from articles published in the givenyear" (Bohlin et al.,2016).The Eigenfactorisalso referred to as arival of the Journal Impact Factor (Reider,2017) that addresses some of the shortcomings of the former (Tüselmann, Sinkovics, and Pishchulov, 2015).Ac riticism of the JournalI mpact Factor refers to the fact that all citations are assigned the samew eight,without taking into account their origin, the journal wheret he citations occur (Bohlin et al., 2016).
Amajor difference between the Eigenfactorand the JournalImpact Factor is that the former uses af ive-year time window and the latter at wo-year window for citations.The broader window should account for citations that appear at al ater stageafter the research has been published (Bohlin et al., 2016).While aJ ournalImpact Factor with af ive-year time window was alsoi ntroduced, it seems to be less common than the JournalImpact Factor with atwo-year time window (Chang,McAleer,a nd Oxley,2013).Another advantage of the Eigenfactor is that self-citations are excluded, which removes scorei nflations from journal opportunistic self-citations (Bohlin et al., 2016;C hang,M cAleer, and Oxley,2 013).
Likewise to the use of anyo therb ibliometric or scientometric indicator,t he Eigenfactors hould not be usedi ni solation, and should be supported, for example, by qualitative expert judgements, something that has been emphasised by the Leiden Manifesto for ResearchM etrics, among others (Hicks et al., 2015).Finally, Bohlin et al. (2016) postulate the most important criterion for evaluatingjournal-based metrics is the robustness of the method regarding the selection of journals.

Calculating the Eigenfactor™ Score
The Eigenfactor scorei si ntended to measure the importance of aj ournal to the scientific community by considering the origin of the incoming citations, and is thought to reflecthow frequentlyana verage researcher would access content from that journal.The Eigenfactor for aj ournal is arriveda tb yaseries of steps (eigenfactor.org).These are elicited below.
First,afive-year cross-citation matrix Z is extracted from the JournalCitation Report (JCR) (clarivate.com).¹ =C itations from journal j in year Y 6 to articles publishedi nj ournal i duringt he five years Y 1 to Y 5 Fori nstance, givent he 2019 JCR, the entries of the cross-citation matrix would be: Z ij =C itations from journal j in 2019 to articles published in journal i during the 2014 to 2018 five-year period.Al onger five-year citation window allows taking into account thatc ertain fieldsd on ot have as rapid citation trends as others and only begin af ew years aftert he articles are published.Fori nstance,t he averagea rticle in al eading cell biologyj ournal might receive 10 -30 citations within the two first years after publishing,while, in contrast, the averagearticle in aleading mathematics journal would do very well to receive two citations over the same period.In this regard, measures that onlyl ook at citations in the first two years after publication (e. g., JournalImpact Factor)can be misleading (if disciplinary differences are not accounted for).
Note that in Z,i ts diagonal elements are set to 0, therebyo mittingj ournal selfcitations.This handleso ver-inflating journals thate ngagei nt he practice of opportunistic self-citation.
In the second step, Z is normalized by the column sums (i.e., by the totalnumber of outgoing citations from each journal) to obtain citation probabilities for each journal  Each year morejournals fromthe Sciences and Social Sciences areindexed in the Journal Citation Report.F or the sake of comparison, in 2016,7 611 "source" journals werei ndexed versus 11,877i n 2019.https://clarivate.com/webofsciencegroup/solutions/journal-citation-reports/(July21,2 020).

Eigenfactor
column-wise to other journals represented by the matrix rows.The resulting matrix is the column-stochastic matrix H,s uch that However,n ot all the journals listedi nHare citedb yo ther journals.These journals will all have 0e ntries in theirc orresponding column j.Fors uch journals, an article vector a with entries a j for each sourcej ournal J is computed as follows: where J Y 1 to Y 5 is the number of articles published by Jinthe preceding five-yearwindow and the denominator is the number of articles published by all sourcejournals in the JCRoverthe same five-year window.Thus all journals with no citation links are uniformlyp opulatedw ith a,transforming H into H′.
Third, as tochastic traversal matrix Pi sd efined following Google'sP age-Rank approach, as follows: Here, e T is arow vector of 1s, where T is the transposefunction, and thus A :e T is a matrix with identical columns each equal to the article vector a.
Under as tochastic process interpretation,² the traversal matrix P defines ar andom walk on the journalcitation network thatiseither atransition with probability α weighted by the entries in H′,i.e.the journalcitation probabilities, or is ajump to an arbitrary journal with probability 1 À weighted by the entries in a, i. e. the proportion of articles published by each journal.Note that without α the traversal will be confined onlytothe nodes with high H′ values.Thus α makes allowance for arbitrary citations not contained in the actual data.At each time instant in the random process P modelling arandomwalk from journal J to journal K,the random variables correspond to matrix values based on the intermediate traversals between journals.Additionally,since P possesses the Markov property³ whereby traversals to K depend only on knowing the present journal J it came from and no prior history, P is aM arkov randomp rocess.
In the fourth and lasts tep, the Eigenfactor scoreo fe ach journal is computed.Formally, the Eigenfactors core EF i of journal i is defined as the percentageo ft he total weighted citations that journal ir eceivesf rom sourcej ournals.Thust he vector of Eigenfactor scores is written as wherev ector Ã is extracted from the stochastic traversal matrix P as its leading Eigenvector.Under the stochastic process interpretationt he Ã vector corresponds to the maximum (also known as steady-state) fraction of time spent at each journalrepresented in P. In the Eigenfactors core, this translatesa st he measure of the journal influencef or weightingc itations.
Consider in Figure 1a ni llustration of the resulting Eigenfactor scores for journals within ac itation network.In the figure, the nodes correspond to journals and the nodes sizes reflect their scaled Eigenfactor scores.T he calculations presented aboverecall two aspects involved in computingthe Eigenfactor score for the selected journal Nature in the figure : (1) citation probabilities from other journals to the journal Nature (contained in matrix H′ described above); and relying on it,(2) astochastic traversal pattern defined by P to Nature.The figure vaguelyd epicts this via the edgesb etween Nature and other journals and from the edge thicknesses reflecting the citation inflow and outflow.In general, for each journal found in the JCRd ata,

Eigenfactor
the Eigenfactor score algorithm uses the structure of the entire network to evaluate the importance of each journal, cutting across all disciplines with self-citations excluded.This corresponds to as imple model of research in which readers follow chains of citations as they movef rom journal to journal.Consequently, journals are considered to be influential if they are citedo ften by other influential journals.

Conclusions
As defined by the inventors of the Eigenfactor, "[s]cholarlyr eferences join journals together in av ast network of citations" (eigenfactor.org[July2 1, 2020]).Givent he sheer amount of journals that have emergedo vert ime,t his citation data has been measured and analyzed to sorta nd classify journals.
In this article, one such metric, namelyt he Eigenfactor, has been presented.Apart from that,the role of this indicator within the scientific community in general has also been addressed.Leveragingthe citation data from ClarivateAnalytics' Journal Citation Reports (JCR), the Eigenfactor ratesj ournals of science and social science accordingt ot he number of incoming citations over af ive-year period, with citations from highlyr anked journals weighted to make al argerc ontribution to the Eigenfactor than those from poorlyr ankedj ournals via ac itation network analysis method inspired from Google'sP ageRank.Different disciplines have different citing practices and different time scales on which citations occur,therefore the Eigenfactor with its five-year citation window overcomes limitations of its contemporary metric the JournalI mpact Factor.This is because the latter kind of metrics with smaller citation time windows can err on the side of assigninghigher ratingstojournals in disciplines with fasterc itation patterns rather than creatinga na llowance for all disciplines and their unique citation patterns.
While metrics might be useful to sortand classify large amountsofdata, the concept of ajournal'simportance alsoraised criticism.Forexample, journal-based metrics might have unintended effects on the research system and individual researchers if evaluations are based on metrics without taking into account qualitative expert judgement.There are alsoi nitiativesb eing carried out that try to visualize research outputs beyond journals, and try to acknowledge several forms of impact (e. g., Hauschke, Cartellieri, and Heller,2 018).Thisa rticle described the Eigenfactor, and mentioned some examples of its role in research systems.

Figure 1 :
Figure 1: Am agnified view (within the whitec ircle lens) of am ap visualization (well-formed.eigenfactor.org[July21, 2020]) of Eigenfactor scores (reflected by the node sizes) as acitation network of journals focusing on the journal Nature (blacknode) computed on asubset of journals in the citation dataf romT homson Reuters' Journal CitationR eports.Fora ll nodes connected to Nature,t he edge thicknesses represent the relativeamount of citation flow (incoming and outgoing) withrespect to it; color-codesc orrespond to different domains foundi nt he datas ubset.