backbone (version 1.2.2)

polytope: Polytope method for finding a matrix that maximizes entropy function

Description

Polytope method for finding a matrix that maximizes entropy function

Usage

polytope(G)

Arguments

G

matrix, an adjacency matrix representing a graph

Value

matrix containing optimal solution to entropy function under constraints

Details

Uses convex optimization via the CVXR-package to find a matrix $M$ that maximizes the entropy function where $M$ satisfies the following constraints: (1) the values of $M$ are between 0 & 1, (2) the row sums of the matrix are equal to the row sums of the original matrix, (3) the column sums of the matrix are equal to the column sums of the original matrix.

This method is utilized in the function sdsm to compute probabilities of an edge existing in a graph. Method is called polytope as it is optimizing over the convex hull of the set of matrices (thought of as vectors) with the same row and column sums as the input.

Examples

# NOT RUN {
polytope(davis)
# }