Computation of the efficiency of a network
g_efficiency(g, diag = FALSE)A single numeric value between 0 (completely inefficient graph) and 1 (maximally efficient graph). The value 0 can occur when the network is disconnected.
This is a function to be able to calculate the
efficiency of a network of class igraph.
The function that does the calculation is
efficiency, which would require the conversion
of the igraph object into a network object
or a non-sparse adjacency matrix.
This current function does the conversion to a non-sparse
adjacency matrix under the hood and then feeds that to
efficiency for the actual calculation.
Edge weights are not included in the algorithm, the graph is dichotomized by default. Make sure to not feed multiplex graphs to the algorithm, as it is not obvious how to define graph efficiency in this case.
From the sna help:
Let G= G_1 U ... U G_n be a digraph with weak components G_1,G_2,...,G_n. For convenience, we denote the cardinalities of these components' vertex sets by |V(G)|=N and |V(G_i)|=N_i, for i in 1,...,n. Then the Krackhardt efficiency of G is given by 1 - ( |E(G)| - Sum(N_i-1,i=1,..,n) )/( Sum(N_i(N_i-1) - (N_i-1),i=1,..,n) ) which can be interpreted as 1 minus the proportion of possible 'extra' edges (above those needed to weakly connect the existing components) actually present in the graph. A graph which an efficiency of 1 has precisely as many edges as are needed to connect its components; as additional edges are added, efficiency gradually falls towards 0.