To compute the 2006 Eigenfactor scores, we proceed as follows. From the Thompson Scientific JCR dataset, we extract a cross-citation
matrix,  for the 7,611
ISI-linked science and social science journals, where  =
number of citations from 2006 articles in journal  to
articles in journal  published
in 2001-2005.
We then zero the diagonal of to ignore journal self-citations.
We now construct a normalized version of ,
named  , normalized by the
column sums, i.e.: the number of outgoing citations from each journal.
We also compute an article vector  , where  is the number of articles
published by journal over the five-year target window, divided by the total
number of articles published by all source journals over the same five-year
window.
Some of the journals listed in the matrix will be dangling nodes —
journals that do not cite any other journals. Any column of the matrix
that has all 0 entries is a dangling node; we replace all such columns in with the vector to produce a new modified matrix  . This is a stochastic matrix by construction. corresponds
to a random walk on the scientific literature as described above
in "A Model of Research." From this, we construct a
new stochastic matrix,  :
 a e^T $)
Where,  is a row vector of all 1's, and thus  is a matrix with identical columns . This corresponds to a process which follows the
literature with probabilities  and
"teleports" to a random journal with weights proportional to the number of articles published by a journal.
Like Google, we use  .
We define the vector  as
the leading eigenvector of which
corresponds to the fraction of time spent at each journal in .
These fractions serve as our weights of journal influence.
The Eigenfactor™ score, EF, is defined as
The Article Influence™ score  for each journal is a measure of the per-article citation influence of the journal. The Article Influence score is calculated as
Where  is the Eigenfactor score for journal and is the -th entry of the normalized article vector.
Further detailed information on our methods is
available here in PDF format. Pseduocode is available here in PDF format.
The modified eigenvector centrality algorithm used to rank
journals
at Eigenfactor.org expands upon a thirty-year tradition of using
iterative methods to quantify the influence of scholarly
publications. The most important predecessors to our work include references [4-9] below. |
The Eigenfactor
In addition to providing direct estimates of how often journals
are likely to be used, this approach offers a number of advantages.
As mentioned above, the Eigenfactor ranking system accounts
for difference in prestige among citing journals, such that
citations from Nature or Cell are valued highly relative to
citations from third-tier journals with narrower readership.
The Eigenfactor score also adjusts for differences in citation
patterns among disciplines. We can see why by looking at our
example of the model researcher. Whether a journal cites 10
other journals or 100, the researcher will follow only one
of those links. This is like a normalized voting system in
which one can vote once with one’s full vote, ten times
with each vote carrying weight 1/10th, or 100 times with each
vote carrying weight 1/100th . Either way, one’s choices
carry the weight of a single vote. 
