Nestedness
Abstract
The methods presented in this page measure the nestedness of a network. Nestedness is usually restricted to biparite networks, although following the arguments laid out by Staniczenko et al. (2013), we consider spectralradius to be a measure of nestedness.
η
Degree distribution and η
The η measure of nestedness is invariant for a given degree distribution. In other words, two networks with the same (joint) degree distribution will always have the same value of η. As a result, network permutations using swap! and a constraint on the degree will not generate an appropriate null sample. This is also true when only one side on the degree distribution is maintained, for the measure of nestedness on this side.
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SpeciesInteractionNetworks.η — Function.
η(N::SpeciesInteractionNetwork{<:Bipartite, <:Union{Binary, Probabilistic}})
The η measure of nestedness is a variation of NODF, at the scale of the entire network. The measure for the entire network is the average of the nestedness of rows and columns.
References
Bastolla, Fortuna, Pascual-García, Ferrera, Luque and Bascompte (2009)
η(N::SpeciesInteractionNetwork{<:Bipartite, <:Union{Binary, Probabilistic}}, dims::Integer)
The η measure of nestedness is a variation of NODF, it can be calculated for either side of the network (1 for rows, 2 for columns).
References
Bastolla, Fortuna, Pascual-García, Ferrera, Luque and Bascompte (2009)
NODF
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SpeciesInteractionNetworks.nodf — Function.
nodf(N::T; dims::Union{Nothing,Integer}=nothing) where {T <: Union{BipartiteNetwork,BipartiteQuantitativeNetwork}}
Returns nodf for a margin of the network. The i argument can be 1 for top-level, 2 for bottom level, and the function will throw an ArgumentError if an invalid value is used. For quantitative networks, WNODF is used.
References
Almeida-Neto, Guimar{ã}es, Guimar{ã}es, Loyola and Ulrich (2008)
Almeida-Neto and Ulrich (2011)
Spectral radius
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SpeciesInteractionNetworks.spectralradius — Function.
spectralradius(N::SpeciesInteractionNetwork{<:Unipartite, <:Binary}; correction=:links)
The spectral radius of a unipartite is a conceptual equivalent to nestedness (Staniczenko et al., 2013). It is defined as the absolute value of the largest real part of the eigenvalues of the undirected adjacency matrix.
There are a number of corrections available through the correction keyword.
The default correction is :links as in Staniczenko et al. (2013), where the values are divided by the square root of the number of links, excluding the self-interactions.
Using the :connectance correction follows the version of Phillips (2011), where the values are divided by the square root of $(L\times(S-1))S^{-1}$ (this is not quite connectance, but the point is that this version is corrected for network size and order).
Using :none returns the raw values, and for the sake of comparisons across networks, it is advised not to use it. It is included for cases where the networks to compare have the same number of species and interactions, as in this case it is appropriate and slightly faster than other corrections.
References
Staniczenko, Kopp and Allesina (2013)
spectralradius(N::SpeciesInteractionNetwork{<:Bipartite, <:Binary}; kwargs...)
The bipartite version of spectralradius is measured by first projecting the bipartite network as a unipartite one using render. The same options as for the unipartite version are then applied.