##### Jevin West

##### Carl Bergstrom

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SubscribeOver the years, we have received numerous questions about the Eigenfactor Metrics. Where did the idea come from? How does the algorithm work? How is it different from Journal Impact Factor? What are other ways the metrics can be used? Below, we will answer a few of these common questions.

### What was the genesis of the Eigenfactor Metrics?

Back in 2006, we introduced the Eigenfactor^{1} Metrics as an alternative way for assessing journal influence. Journal Impact Factor was the common currency of journal evaluation back then, and it still is today. It has a simple formula, and, although not perfect, does a reasonable job at approximating relative journal influence. Our goal was to improve upon this measure.

During the late 1990s, the growth of the web was exploding, as was the need for good search engines. Due to several innovations, Google emerged as the big winner. There are many reasons for its success, but one reason was their core algorithm, PageRank. It simply worked.

The primary input for PageRank was the hyperlinks connecting webpages. This hyperlink structure reveals a lot about which websites are important and which ones are not. Websites linked to by other important websites (i.e., linked to by important websites) rank high. This may sound circular, but this process is mathematically well defined. This algorithm is now one of the most famous applications of Markov theory and a basic tenet of any computer science education.

Journal citation networks closely resemble the World Wide Web. Journals represent nodes (websites) and citations represent links (hyperlinks). We were inspired by the effectiveness of PageRank in ranking websites so we decided to develop a variant of PageRank for journals. The result was the Eigenfactor™ Score and Article Influence™ Score. The underlying philosophy was that highly influential journals will be cited by other influential journals.

After developing the metric and calculating them on the *Journal Citation Reports* (JCR), we spent countless hours examining these new journal rankings. We were amazed at how well it seemed to work, especially across disciplines. For example, in the field of Economics, Journal Impact Factor was criticized for ranking Health Economic journals over the top Economic journals in the field. It does this because it simply counts citations, and health journals tend to include more references per paper than traditional economic journals. The Eigenfactor Metrics corrects for this. The algorithmic mimics a random walk on the citation network. If a journal has a lot of out-citations, then each citation has less of a chance of being followed by the random walker in each visit to that journal. These kinds of corrections help normalize differences in citation cultures across different disciplines and multidisciplinary journals.

### What is the difference between Eigenfactor and Article Influence?

If there is one thing we could change, it would be naming the Article Influence Score the “Eigenfactor Score” and the Eigenfactor Score something else. But so it goes. Of the two measures, the Article Influence Score is most frequently used because it normalizes by the size of the journal, similar to how Journal Impact Factor divides by the number of articles. The Eigenfactor Score is the total influence of a journal similar to how citation counts scale. Bigger journals tend to have bigger Eigenfactor Scores, just as they would with raw citation counts. Since we call the measures the Eigenfactor Metrics, users get confused on the differences between the two metrics.

Both measures utilize the structure of the citation network. The time window for both measures is 5 years. The difference is that the Eigenfactor Score measures the total influence of a journal, and the Article Influence Score takes into account the size of the journal. Eigenfactor is additive, which means one can add Eigenfactor scores for different journals together to get a total influence score. All else being equal, the Eigenfactor Score will increase with size (i.e., the number of articles published per year) of a journal.

The Article Influence Score measures the influence, per article. Some journals don’t publish a lot of articles but each article may be highly influential. The Article Influence Score is calculated by dividing the Eigenfactor Score by the number of articles of that journal and normalizing the scores so that the average score equals 1. That means if a journal has a score of 5, it will be 5 times as influential as the average journal. The Article Influence Score is comparable to Journal Impact Factor, whereas the Eigenfactor Score is comparable to total citation counts.

More details on the algorithm and comparing the different measures can be found at the Eigenfactor website and in the following papers:

**The Eigenfactor™ Metrics: A network approach to assessing scholarly journals**

J.D. West, T.C. Bergstrom, C.T. Bergstrom, (2010)*College and Research Libraries. 71(3): 236-244 * [pdf]

**Big Macs and Eigenfactor Scores: Don't Let Correlation Coefficients Fool You**

J.D. West, T.C. Bergstrom, C.T. Bergstrom, (2010)* Journal of the American Society for Information Science & Technology. 61(9): 1800-1807* [pdf]

** Author-Level Eigenfactor Metrics: Evaluating the Influence of Authors Institutions and Countries Within the SSRN Community.**

J.D. West, M.C. Jensen, R.J. Dandrea, G.J. Gordon, and C.T. Bergstrom, (2013)* Journal of the American Society of Information Science and Technology 64: 787-80*1 [pdf]

### What is the new Normalized Eigenfactor (nEF) Score?

Over the years, we have found that users have a difficult time interpreting the Eigenfactor Score, especially because of the small decimal numbers used for the scores. The Eigenfactor Score for all journals in the JCR adds up to 100. That means the 11,000 or so journals in the JCR have to share their score with everyone else. That makes for very small numbers for most journals. If they all had the same score, the value would be 0.01. Given that some journals (e.g., *Nature* and *Science*) own a significant portion of all the Eigenfactor Score, many of the journals will have very small scores.

To improve the interpretation and to reduce the decimal dominance, we modified the Eigenfactor Score. The modification is simple: we multiply each Eigenfactor Score by 1/100 and then multiply those numbers by the total number of journals in the JCR. That way, one can interpret the journal score simply as a multiple of the average score in the JCR, which is 1. For example, if a journal had a nEF of 5, this would mean that this journal is 5 times as influential as the average journal in the JCR. This modification makes the scores more easily digestible and now parallels the Article Influence Score’s multiplicative interpretation.

The good news is that this modification does not change the relative order of the journals. Some like to use percentiles for the journals, and these orders will not change with this modification. We only multiply by a constant so the ordinal rankings are the same and the cardinal value only changes by a multiplicative scalar.

### What is the relationship with Clarivate Analytics?

People have asked us about our relationship with Thomson Reuters, now Clarivate Analytics. Do we receive funding to for calculating these metrics? No, we have never received funding from Thomson Reuters or Clarivate Analytics for the Eigenfactor Metrics. We have a data agreement. Clarivate Analytics shares with us the raw citation data and we calculate scores that are published in the JCR. We see this as a collaborative endeavor. Clarivate Analytics produces the highest-quality citation databases that we can use to calculate the Eigenfactor Metrics, which are then used in research projects using this data.

### What is next for the Eigenfactor Metrics?

The Eigenfactor Metrics is just one aspect of the Eigenfactor Project. The project also includes work on mapping scientific domains, which lead to work on the MapEquation project; the cost effectiveness project, which analyzes and builds tools for comparing open access journals using the Article Influence Score; the well-formed project, which designs interactive visualizations for exploring citation networks; the sociology of science work and gender work, which uses the citation structure to ask questions about gender representation in science; ranking article-level citation networks, which can be used to rank other time-directed networks; and the recommendation work, which uses the Eigenfactor algorithm to recommend articles and journals. Each of these projects utilizes the structure of citation networks to ask questions and build new tools.

More information can be found at Eigenfactor.org. If you have questions, please feel free to contact us.

^{1}The name is the amalgam of eigenvector centrality – a common method in linear algebra – and a play on Journal Impact Factor.