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does not preferentially aggregate hubs, but decays also as a
power law of k
Γ
, which agrees with 92% of nodes in Γ with
k
Γ
< 20. As a result, the hub-and-spoke pattern guarantees
minimal, but sufficient, network control of the information
flow, limiting the system in the transition between assorta-
tive and disassortative regimes towards the latter. Currently,
the solution γ ~ 2 and µ ≤ 0 found for Embrapa seems driven
by the system self-adaptation to minimize Γ that gathers
about 14% of internal collaborators, principally males (con-
tingence table in Sect.3 of the Appendices).
Scale-free networks lying on γ ~ 2 minimize Γ because
the trivial upper limit of Γ is described by n ~ k
max
, where
k
max
is the highest degree of a network [5]. However, Γ is
minimized for µ < 0 in which hubs are separated and can
independently rule many of low-degree nodes. Alternatively,
low-degree nodes also likely obtain advantages by connect-
ing at least to a single hub [39] for, e.g., paced promotions,
considering the functional stability in the Brazilian public
services.
On the other hand, network control seems useful to focus
on TRL [28] to strengthen collaboration and innovation
with the private sectors [29, 30]. The ability to control the
information flow, however, may bring also implications for
the institutional efforts to boost innovation in open science
based, e.g., on FAIR (findability, accessibility, interoper-
ability, and reuse of digital assets) principles [41]. Conse-
quently, current optimization problems seem associated with
minimal but sufficient organizational changes.
Definitely, more incentives may be necessary to exploit
the potential benefits of multidisciplinary diversity in stim-
ulating more intra-organizational research collaborations
that span disciplinary (and regional) boundaries [40]. For
instance, the current division of Embrapa’s units in three
major types (product, ecoregional and thematic) that favors
competition and isolation could benefit from only one or
two labels aligned to a TRL model—e.g., innovation and
business centers—focused on a few portfolios and mixed or
not with external RD&I associates [26].
An interesting example is the system adopted by the
USDA-ARS, which has physical bases (laboratories) at
universities, working in an integrated manner on specific
research topics [24]. In addition, the programmatic figure of
portfolios is very welcome because it replaces the current
strategy of decentralized units with national missions for
the coordination of large product chains, as well as making
it possible to act on transversal themes in various regions of
the country [27].
In general, organizations have formal and informal
structures. Collaboration is distributed laterally due to
more capacity, transparency and trust, rendered as human
capital [42]. On the other hand, human capital in hierarchi-
cal topologies is asymmetrical and routinely concentrates
between superiors and subordinates [18, 43]. Consequently,
for increasing the pace of innovation, a widespread increase
in human capital ought to be considered throughout the
entire network [42]. Furthermore, an increase in the role
of gatekeeper agents, which is now restricted for analyst
females, may ease the establishment of innovation by bridg-
ing organization’s units.
Lastly, a multidisciplinary organization demanding more
innovation capacity in infodemic societies [3, 4] needs to
seek for new formal and informal rules that optimize degree
and correlation degree distributions toward γ ≥ 2 and µ ≥ 0,
respectively. As communication (network edges) grows, it
seems reasonable to allocate efforts to strengthen the auton-
omy of the nodes [42] instead of increasing the controllabil-
ity of information [44, 45].
Conclusions
The topological study of the scientific collaboration net-
work of Embrapa indicates that nodes degree distribution
is scale free and forms a giant component, whereas nodes
degree correlation suggests a disassortative regime. A hub-
and-spoke topology likely emerges from competition and
minimal but sufficient network control, which may, however,
prevent a required increment in innovation capacity.
Jobs of controller and researcher are twice as many occu-
pied by males, except for the jobs of analysts, who act as
network gatekeepers, as indicated by the measure of close-
ness centrality. Product units show greater affinity to form
clusters than ecoregional or thematic units that, in turn, tend
to concentrate hubs at the inner core of the giant component.
With the largest number of individuals in product units, the
South region tends to develop more collaborative clusters.
Alternatively, hubs located in thematic and ecoregional units
in the Midwest region have greater gravitational force, posi-
tioning themselves at the inner core of the giant component.
Combining the improvement in human capital with the uni-
versalization in the labeling of units can motivate a multi-
disciplinary organization to share knowledge and hasten the
pace of innovation internally and with external associates.
A clear limitation of this work is that it considers only a
snapshot of the current state of scientific collaboration of the
studied organization, and an evolutionary network approach
would bring more insightful information regarding, e.g., the
reasons for reaching the actual topological shape. In any
case, the preliminary deciphering of the current network
topology by network science remains a new contribution,
as, to date, a network study of all of Embrapa’s scientific
collaboration has not been carried out.
Acknowledgements The authors thank to Embrapa for providing open
data that supported this work. The anonymous dataset explored in this
research can be available on request to the corresponding author.