In 1977, Freeman developed a set of centrality measures based on betweenness [58].
The plugin NetworkAnalyzer (Assenov et al., 2008; Doncheva et al., 2012b) and the Java application CentiBiN (Junker et al., 2006) feature a large set of centrality measures, but they cannot compute the measures for a user-defined set of seed nodes or for weighted networks.
This perspective poses serious concerns on the minimum and optimal set of centralities that are needed to characterize functional properties of the network nodes (e.g., proteins, genes).
Finally, we tested the performance of smaller subsets of centralities (composed of 4 indices) to determine whether the same proteins could be identified as with the full set of centralities.
While the built-in NetworkAnalyzer tool is oriented in characterizing the global behaviour of the network, provided with several global network statistics, CentiScaPe is designed to identify the most relevant nodes and provides a more comprehensive set of centralities.
The last row summarizes results obtained with the whole set of 6 centralities.
The set of degree centralities, which represents the collection of degree indices of N actors in a network, can be summarised by the following equation to measure network degree centralisation[ 47]: (3) C D = ∑ i = 1 N C D n * − C D n i N − 1 N − 2 Where, { C D (n i )} are the degree indices of N actors and C D (n*) is the largest observed value in the degree indices.
The betweenness centrality (with respect to the nodes in the seed set) is a measure of centrality of a node in a network [ 40].
Again, if the distribution for the last five sets is biased toward higher values of centrality than the distribution for the first set, we could hypothesize that B. anthracis, F. tularensis, and Y. pestis have evolved to interact with proteins with high betweenness centrality in the human PPI network.
We compared the performance of both methods under 20 sets of thresholds for betweenness centrality and degree; the results are shown in Table 4.
