infoTheoreticGCM: Information theoretic graph complexity meassures
In QuACN: QuACN: Quantitative Analysis of Complex Networks

Description Usage Arguments Details Value Author(s) References Examples

Measures of this group assign a probability value to each vertex of the network using a so-called information functional f which captures structural information of the network g. Note that some combinations of the settings can cause the descriptor to retrun NaN. In that case you have to check for warnings.

1 2	infoTheoreticGCM(g, dist = NULL, coeff = "lin", infofunct = "sphere", lambda = 1000, custCoeff=NULL, alpha=0.5, prec=53, flag.alpha=FALSE)

`g`	a graph as a graphNEL object.
`dist`	the distance matrix of the graph. If the parameter is empty the distance matrix will be calculated within the function.
`coeff`	specifies the weighting coefficient. Possible values are "lin" (default), "quad", "exp", "const" or "cust". If it is set to "cust" you have to specify your customized weighting schema with the parameter custCoeff.
`infofunct`	specifies the information functional. Possible values are "sphere" (default), "pathlength", "vertcent" or "degree" .
`lambda`	specifies the scaling constant for the distance measures. The default value is 1000.
`custCoeff`	specifies the customized weighting schema. To use it you need to set coeff="const".
`alpha`	alpha for degree degree association.
`prec`	specifies the floating-point precision to use (currently only implemented for degree-degree association). Values up to 53 are handled with the built-in double data type; larger values trigger the usage of Rmpfr.
`flag.alpha`	if set, the base 0.5 exponential function will be applied to the values of the "sphere" functional.

For details see the vignette.

The returned list consists of the following items:

`entropy`	contains the calculated entropy measure.
`distance`	contains the calculated distance measure.
`pis`	contains the calculated probability distribution.
`fvi`	contains the calculated values of the information functional, for each vetrex.

If any of these values is NaN, please check if your parameters are valid. For infofunct="degree" in particular, the result might be impossible to represent using a standard R numeric vector. In this case the "prec" parameter has to be set to a higher value.

If infofunct is "degree" and prec is greater than 53, the resulting values will be of class "mpfr" (instead of "numeric" in all other cases). Note that if you use such a vector in a calculation, arbitrary precision floating point arithmetics will be used throughout, even if the other operands are regular double values. You can use "as.double" at any point to convert an "mpfr" vector to the built-in "numeric" class (losing precision).

Laurin Mueller

M. Dehmer, Information processing in complex networks: Graph entropy and information functionals, Applied Mathematics and Computation, 202:82-94, 2008

Dehmer M., Emmert-Streib F., Tsoy R. Y., Varmuza K.: Quantifying Structural Complexity of Graphs: Information Measures in Mathematical Chemistry. In: Putz M. (Editor): Quantum Frontiers of Atoms and Molecules in Physics, Chemistry, and Biology, Nova Science Publishers, to appear, 2010

library(RBGL)
set.seed(123)
g <- randomGraph(1:8, 1:5, 0.36, weights=FALSE)
mat.dist <- distanceMatrix(g)

infoTheoreticGCM(g)
infoTheoreticGCM(g,mat.dist,coeff="lin",infofunct="sphere",lambda=1000)
infoTheoreticGCM(g,mat.dist,coeff="const",infofunct="pathlength",lambda=4000)
infoTheoreticGCM(g,mat.dist,coeff="quad",infofunct="vertcent",lambda=1000)
infoTheoreticGCM(g,mat.dist,coeff="exp",infofunct="degree",lambda=1000)