BrainNetVis: An Open-Access Tool to Effectively Quantify and Visualize Brain Networks
Table 1
Network and vertex metrics available in BrainNetVis.
Zhang and Horvath
The weights have been normalized by .
The above definition uses only the network values, in the context of gene coexpression networks.
Onnela
Here, the edge values are normalized by the maximum value in the network,
.
Assortative mixing
Symmetrical weighted networks
Directed weighted networks
is the sum of all values of edges in .
Degree centrality of vertex v
Undirected binary network
Degree of vertex
Directed binary network
In-degree
Out-degree
Strength centrality
Greyscale symmetric network
Strength of vertex
Greyscale assymetric network
In-strength:
Out-strength:
Shortest-path Efficiency
, where
Shortest-path Betweeness centrality of a vertex
, where is the number of shortest -paths
is the number of shortest -paths passing through some vertex other than , and is a normalizing constant.
Bonacich's eigenvector centrality
In matrix notation with , this yields:
.
This type of equation is well known and solved by the eigenvalues and eigenvectors of .
We call the eigenvector of the maximal eigenvalue of principal eigenvector. Then, the eigenvector centrality of node is defined as: ,
where the centrality vector is normalized by dividing it by its -norm
and to produce centrality scores .
Hubbell's centrality
where and .
In order to get meaningful results, should be chosen according to restriction , where is the maximum value of an eigenvalue of .
This restriction is not mentioned in the literature.
Subgraph centrality of vertex
It is given by the th diagonal entry of the th power of the adjacency matrix,
with number of closed walks: .
This measure generalizes to greyscale networks by substituting matrix for .
Network entropy
To produce the above equation, we have set a Markov matrix be the stochastic process which defines the information source and its stationary distribution .
