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Analysing the sensitivity of nestedness detection methods
Many bipartite and unipartite real-world networks display a nested structure. Examples
pervade different disciplines: biological ecosystems (e.g. mutualistic networks),
economic networks (e.g. manufactures and contractors networks) to financial networks
(e.g. bank lending networks), etc. A nested network has a topology such that a vertex’s
neighbourhood contains the neighbourhood of vertices of lower degree; thus –upon
vertex reordering– the adjacency matrix is step-wise. Despite its strict mathematical
definition and the interest triggered by their common occurrence, it is not easy to
measure the extent of nested graphs unequivocally. Among others, there exist three
methods for detection and quantification of nestedness that are widely used:
BINMATNEST, NODF, and fitness-complexity metric (FCM). However, these methods fail
in assessing the existence of nestedness for graphs of low (NODF) and high (NODF,
BINMATNEST) network density. Another common shortcoming of these approaches is
the underlying assumption that all vertices belong to a nested component. However,
many real-world networks have solely a sub-component (i.e. a subset of its vertices)
that is nested. Thus, unveiling which vertices pertain to the nested component is an
important research question, unaddressed by the methods available so far. In this
contribution, we study in detail the algorithm Nestedness detection based on Local
Neighbourhood (NESTLON). This algorithm resorts solely on local information and
detects nestedness on a broad range of nested graphs independently of their nature
and density. Further, we introduce a benchmark model that allows us to tune the
degree of nestedness in a controlled manner and study the performance of different
algorithms. Our results show that NESTLON outperforms both BINMATNEST and NODF.
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E-Jurnal
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Statement of Responsibility |
Alexander Grimm 1,2* , Claudio J. Tessone 1,2
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