Author
Salnikov, V
Cassese, D
Lambiotte, R
Jones, N
Journal title
Applied Network Science
Last updated
2024-03-24T19:08:11.303+00:00
Abstract
In the last years complex networks tools contributed to provide insights on
the structure of research, through the study of collaboration, citation and
co-occurrence networks. The network approach focuses on pairwise relationships,
often compressing multidimensional data structures and inevitably losing
information. In this paper we propose for the first time a simplicial complex
approach to word co-occurrences, providing a natural framework for the study of
higher-order relations in the space of scientific knowledge. Using topological
methods we explore the conceptual landscape of mathematical research, focusing
on homological holes, regions with low connectivity in the simplicial
structure. We find that homological holes are ubiquitous, which suggests that
they capture some essential feature of research practice in mathematics. Holes
die when a subset of their concepts appear in the same article, hence their
death may be a sign of the creation of new knowledge, as we show with some
examples. We find a positive relation between the dimension of a hole and the
time it takes to be closed: larger holes may represent potential for important
advances in the field because they separate conceptually distant areas. We also
show that authors' conceptual entropy is positively related with their
contribution to homological holes, suggesting that polymaths tend to be on the
frontier of research.
Symplectic ID
830635
Download URL
http://arxiv.org/abs/1803.04410v1
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Publication type
Journal Article
Publication date
28 Aug 2018
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