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citation then there is also a possibility that more then one indirect citation paths
can be found. In this case we would like to study all paths to certain length lying be-
tween our recent - reference - publication and the core book. The vertices on these
paths form a set of publications that deserve a further study of their importance
by the user.
For our experiment we have chosen [11] as the reference publication. We de-
ployed the
ρ
-index on our testing citation graph and searched for all paths to
length 10. From the nature of the
ρ
-index that we discussed earlier in this chapter
we got all the paths to the length of 10 and some longer. Table 10.1 summarizes
the amounts of paths found according to their length and a total number of
distinct vertices of all paths up to that length. Figure 10.16 demonstrates the
network of the paths up to length 6 - as a length of a path we mean the num-
ber of vertices in a path. In that figure, the vertices represent publications that
are placed on the background of a timeline to make the result more readable.
Although, the
ρ
-index was created to index all the paths up to the length of
10 and as Table 10.1 shows
ρ
-index does index also some more, Figure 10.16
demonstrates only the paths to the length 6 since it would get very hard to
follow when it have contained all the paths got from the
ρ
-index.
As can be seen in Figure 10.16, the result of the search is a network with one
source which is our reference publication and one sink which represents our core
publication. The result presents a chosen set of publications from the citation
graph which relate to the reference publication because the reference publica-
tion indirectly cites them and they relate to the field of information retrieval
since they indirectly cite our core publication. The resulting publications are or-
dered according to the year of their publication. Yet another ranking technique
could be used to study the relevancy between the reference publication and the
publication found using
ρ
-index but that is beyond the scope of this chapter.
The approached proposed used one core publication and as we seen we got
for this one a fair amount of publications from the citation graph because the
core publication is well known. If we used as a core publication not so well-
known publication the system would not be able to retrieve a reasonably big
set of publications. For this reason the approach could be improved to carry out
the search with only one core publication but with a set of core publications.
Consequently,
ρ
-index would find all the paths to each particular publication
from the core set and put the result together. This improvement brings another
interesting issue since the retrieved networks can overlap and that information
can be also used for further recommendation process.
10.6
Concluding Remarks and Future Work
Our goal was to design an indexing structure that would make possible an ef-
fective discovery of paths having special properties in a large graph. The first
objective was to find all paths to certain length
l
between any two vertices. Also
we still get some amount of paths longer than the specified
l
as an approximation.
