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where
A
(
i
) is the number of documents authored by
a
i
and
A
(
i
,
j
) represents the
number of documents coauthored by
a
i
and
a
j
.
l
Citation
. This social relationship is represented by a directed edge connecting an
author with his cited authors. An author who usually cites a second author would
be influenced by his opinions and eventually discuss similar subjects. Therefore,
the citation links expresses knowledge transfer between authors. To evaluate
citation relationship strength, we propose to take into consideration the citation
frequency, as well as the total announced citations. Citation relationships is
weighted as follows:
C
ð
i
j
Þ
;
Ci
ð
i
j
Þ¼
(6.2)
;
;
C
ð
j
Þ
where
C
(
i
) is the number of citations announced by author
a
i
and
C
(
i
,
j
)
represents the number of times author
a
i
cites
a
j
.
This social relationship is represented by a directed edge connecting an
author with his authored documents. The strength of the authorship association
is viewed as the author affiliation with the topic of the document. We note that an
author would be more affiliated with a topic if he frequently addressed it in his
published papers. Therefore, a coauthor will be more associated with document
d
discussing a topic
S
rather than all his coauthors if he has published more
documents in this topic.
In order to estimate the knowledge and the experience of a coauthor
a
k
2
A
on
the topic of document
d
, we propose to compare the quantity of information he has
imported via his other publications. From the information producer's point of view,
this can be measured by the information entropy
H
d
ð
fortagsassignedtothe
subset of the coauthor publications noted
A
k
. We consider as a random variable
each tag
t
i
2
t
i
Þ
T
d
assigned to document
d
where it exists an edge
e
(
t
i
,
d
j
)
D
)
and we calculate its probability distribution Pr
k
(
t
i
) among the subcollection of
documents
2
(
T
A
¼
S
k¼
1
A
k
published by the
m
coauthors of the document
d
.
We propose to normalize the information entropy values by the number of
tags associated with the document noted
T
d
. Meanwhile, a coauthor with a
single publication in the collection has
H
d
ð
t
i
Þ¼
0 and gets a higher weight value
1 rather than his coauthors with much more publications on the topic
of the document. We propose so to assign a default weight value for authors
having unique document in the dataset and take into consideration the number of
publications per author.
l
Authorship
. This social relationship is represented by a directed edge connecting
an author with his authored documents. The strength of the authorship associa-
tion is viewed as the author affiliation to the topic of the document. We note that
an author would be more affiliated with a topic if he frequently addressed it in his
published papers. Therefore, a coauthor will be more associated with document
d
discussing a topic
S
rather than all his coauthors if he has published more
documents in this topic.
w
ð
a
i
;
d
j
Þ¼
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