From Ecology to Finance (and Back?): A Review on Entropy-Based Null Models for the Analysis of Bipartite Networks

Nestedness is a statistical measure used to interpret bipartite interaction data in several ecological and evolutionary contexts, e.g. biogeography (species-site relationships) and species interactions (plant-pollinator and host-parasite networks). Multiple methods have been used to evaluate nestedness, which differ in how the metrics for nestedness are determined. Furthermore, several different null models have been used to calculate statistical significance of nestedness scores. The profusion of measures and null models, many of which give conflicting results, is problematic for comparison of nestedness across different studies. We developed the FALCON software package to allow easy and efficient comparison of nestedness scores and statistical significances for a given input network, using a selection of the more popular measures and null models from the current literature. FALCON currently includes six measures and five null models for nestedness in binary networks, and two measures and four null models for nestedness in weighted networks. The FALCON software is designed to be efficient and easy to use. FALCON code is offered in three languages (R, MATLAB, Octave) and is designed to be modular and extensible, enabling users to easily expand its functionality by adding further measures and null models. FALCON provides a robust methodology for comparing the strength and significance of nestedness in a given bipartite network using multiple measures and null models. It includes an “adaptive ensemble” method to reduce undersampling of the null distribution when calculating statistical significance. It can work with binary or weighted input networks. FALCON is a response to the proliferation of different nestedness measures and associated null models in the literature. It allows easy and efficient calculation of nestedness scores and statistical significances using different methods, enabling comparison of results from different studies and thereby supporting theoretical study of the causes and implications of nestedness in different biological contexts.

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Popularity Bias in Bipartite Networks: Efficiency, Errors, and Fake Views

SSRN Electronic Journal ◽

10.2139/ssrn.3686145 ◽

2020 ◽

Author(s):

Nabil Afodjo ◽

Roland Pongou

Keyword(s):

Bipartite Networks

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The configuration model

10.1093/oso/9780198805090.003.0012 ◽

2018 ◽

Author(s):

Mark Newman

Keyword(s):

Degree Sequence ◽

Graph Model ◽

Network Models ◽

Clustering Coefficient ◽

Giant Component ◽

Configuration Model ◽

Bipartite Networks ◽

Small Component ◽

Random Graph Model ◽

Average Size

A discussion of the most fundamental of network models, the configuration model, which is a random graph model of a network with a specified degree sequence. Following a definition of the model a number of basic properties are derived, including the probability of an edge, the expected number of multiedges, the excess degree distribution, the friendship paradox, and the clustering coefficient. This is followed by derivations of some more advanced properties including the condition for the existence of a giant component, the size of the giant component, the average size of a small component, and the expected diameter. Generating function methods for network models are also introduced and used to perform some more advanced calculations, such as the calculation of the distribution of the number of second neighbors of a node and the complete distribution of sizes of small components. The chapter ends with a brief discussion of extensions of the configuration model to directed networks, bipartite networks, networks with degree correlations, networks with high clustering, and networks with community structure, among other possibilities.

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Mathematics of networks

10.1093/oso/9780198805090.003.0006 ◽

2018 ◽

Author(s):

Mark Newman

Keyword(s):

Random Walks ◽

Adjacency Matrix ◽

Graph Partitioning ◽

Dynamic Networks ◽

Graph Laplacian ◽

Network Visualization ◽

Final Part ◽

Bipartite Networks ◽

Component Structure ◽

Basic Properties

An introduction to the mathematical tools used in the study of networks. Topics discussed include: the adjacency matrix; weighted, directed, acyclic, and bipartite networks; multilayer and dynamic networks; trees; planar networks. Some basic properties of networks are then discussed, including degrees, density and sparsity, paths on networks, component structure, and connectivity and cut sets. The final part of the chapter focuses on the graph Laplacian and its applications to network visualization, graph partitioning, the theory of random walks, and other problems.

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P-Simrank: Extending Simrank to Scale-Free Bipartite Networks

Proceedings of The Web Conference 2020 ◽

10.1145/3366423.3380081 ◽

2020 ◽

Cited By ~ 1

Author(s):

Prasenjit Dey ◽

Kunal Goel ◽

Rahul Agrawal

Keyword(s):

Bipartite Networks ◽

Scale Free

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Entropic measure unveils country competitiveness and product specialization in the World trade web

Scientific Reports ◽

10.1038/s41598-021-89519-3 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Gianluca Teza ◽

Michele Caraglio ◽

Attilio L. Stella

Keyword(s):

Iterative Scheme ◽

Entropy Function ◽

Bipartite Networks ◽

Complexity Measures ◽

Wide Range ◽

Self Consistent ◽

Set Up ◽

Technical Features ◽

Country Competitiveness ◽

Entropic Measure

AbstractWe show how the Shannon entropy function can be used as a basis to set up complexity measures weighting the economic efficiency of countries and the specialization of products beyond bare diversification. This entropy function guarantees the existence of a fixed point which is rapidly reached by an iterative scheme converging to our self-consistent measures. Our approach naturally allows to decompose into inter-sectorial and intra-sectorial contributions the country competitivity measure if products are partitioned into larger categories. Besides outlining the technical features and advantages of the method, we describe a wide range of results arising from the analysis of the obtained rankings and we benchmark these observations against those established with other economical parameters. These comparisons allow to partition countries and products into various main typologies, with well-revealed characterizing features. Our methods have wide applicability to general problems of ranking in bipartite networks.

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