# graphCorr: One minus graph correlation matrix

### Description

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

### Usage

 1 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.

graphDist for inverse of the geodesic distance matrix.

### Examples

 1 2 3 4 5 6 7 8 # 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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