One minus graph correlation matrix

Description

graphCorr computes the dissimilarity matrix (one minus the correlation matrix) of a graph structure.

Usage

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graphCorr(A, nodesDegree = NULL)

Arguments

A

matrix or Matrix object with adjacency matrix of a graph.

nodesDegree

vector with nodes degree (in case it is been previously calculated).

Details

The similarity matrix of a graph is given by

σ_{ij} = \frac{η_{ij}}{√{k_ik_j}},

where η_{ij} is defined by the number of common neighbors of nodes i and j and k_i is the degree of the node i. The dissimilarity matrix is given by

δ_{ij} = 1- σ_{ij}.

Value

a dissimilarity lower triangular matrix with one minus the correlation of the graph nodes.

Author(s)

Caballe, Adria <a.caballe@sms.ed.ac.uk>, Natalia Bochkina and Claus Mayer.

References

Costa, L. and F. Rodrigues (2007). Characterization of complex networks: A survey of measurements. Advances in Physics 56(1), 167-242.

See Also

graphDist for inverse of the geodesic distance matrix.

Examples

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# example to use of graphCorr function
EX1         <- pcorSimulator(nobs = 50, nclusters = 2, nnodesxcluster = c(40,30), 
                             pattern = "powerLaw")
y           <- EX1$y
out3        <- huge(y, method = "mb", lambda = 0.4)
gc          <- graphCorr(out3$path[[1]])
  
 

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