M. G. ROSA ET AL.

OPEN ACCESS SN

configuration of disconnected cliques. The results in

Table 2 show that the GP Network displays a higher

variance of density index score higher than the ME Net-

work. The theoretical maximum value for the variance of

density occur s when the network becomes a single clique,

i.e., all of the vertices are mutually connected. For the

ME Network, this maximum value is approximately

2200, and thus the value found herein (7.8784) corres-

ponds to only 0.4% of the maximum. In the case of the

GP Network, the maximum variance of the density is

1223, and the measured value (15.4440) is 1.3% of the

maximum. Comparatively, it can be stated that the GP

Network is more than threefold “densified” compared to

the ME Network. The variance of density index reflects

the coalescence of the authors that published alone but

also as coauthors (reduction of vertices without a reduc-

tion in the number of edges) in relation to the coales-

cence of pairs that published as coauthors (simultaneous

reduction of vertices and edges). To more precisely de-

termine what type of situation predominates in the net-

work, the superposition of edges and the vertex reduction

factor can be used.

The superposition of edges determines the proportion

of coauthor pairs in common; i.e., it is an index that

measures relationships, represented by the edges in the

network. The superposition of approximately 10% in the

ME Network indicates that few pairs of authors pub-

lished together more than once, unlike the GP Network,

where 52% of the pairs have more than one publication

together. This index, therefore, shows that there is more

scientific production by pairs of authors in the GP Net-

work than in the ME Network.

The vertex reduction factor, in turn, is directly related

to the author/vertex ratio in Ta bl e 1 . This index indicates

the percentage of authors with more than one publication.

The values obtained for the ME and GP networks indi-

cate that the researchers in the GP network display higher

individual productivity.

The values of the component reduction factor for the

two networks do not differ. Although the ME Network

has 160 components compared to only 08 for the GP

Network , the percentage difference is approximately

12%. However, almost all of the coauthorship groups

shared at least one vertex in common (link) in the GP

Network (99.4%), while a value of 87.4% was observed

in the ME Network.

6. Final Considerations

The clique approach in coauthorship networks allows the

social data to be analyzed in a way that is well suited for

the network topological structure. Network analysis us-

ing cohesion indices already allows new interpretations.

For example, considering the index that measures edge

superposition together with the vertex reduction factor

allowing us to clarify h ow the juxtaposition an d superpo-

sition processes create the network. Thus, we observed

that superposition predominated in the GP Network

compared to the ME Network. This effect also occurred

with the vertex reduction factor, but to a lesser extent.

These aspects result in a greater “densification” of the

GP Network, mostly due to the large number of pairs of

authors who have written more than one study together.

These results are consistent with the fact that the GP

Network comprises researchers connected through the

same research institution, while the ME Network in-

cludes researchers who may have stronger ties within

their own groups, but this collaboration is not shown

through their publication in jou rn a ls of the field .

The initial research us ing cohes ion indices showed that

other indices could potentially be added, and the dynam-

ics of network growth could be evaluated. Another aspect

that we emphasize is the applicability of the clique ap-

proach to other social networks with a similar structure,

such as actor-movie networks.

Finally, it is important to comment that th is work is an

ongoing research and initially it was published in the

proceedings of the 1st Brazilian Workshop on Social

Network Analysis and Mi ning [13].

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