fundamentalNetworkConcepts {WGCNA}

Calculation of fundamental network concepts from an adjacency matrix.

Description

This function computes fundamental network concepts (also known as network indices or statistics) based on an adjacency matrix and optionally a node significance measure. These network concepts are defined for any symmetric adjacency matrix (weighted and unweighted). The network concepts are described in Dong and Horvath (2007) and Horvath and Dong (2008). Fundamental network concepts are defined as a function of the off-diagonal elements of an adjacency matrix adj and/or a node significance measure GS.

Usage

fundamentalNetworkConcepts(adj, GS = NULL)

Arguments

adj

an adjacency matrix, that is a square, symmetric matrix with entries between 0 and 1

GS

a node significance measure: a vector of the same length as the number of rows (and columns) of the adjacency matrix.

Value

A list with the following components:

Connectivity

a numerical vector that reports the connectivity (also known as degree) of each node. This fundamental network concept is also known as whole network connectivity. One can also define the scaled connectivity K=Connectivity/max(Connectivity) which is used for computing the hub gene significance.

ScaledConnectivity

the Connectivity vector scaled by the highest connectivity in the network, i.e., Connectivity/max(Connectivity).

ClusterCoef

a numerical vector that reports the cluster coefficient for each node. This fundamental network concept measures the cliquishness of each node.

MAR

a numerical vector that reports the maximum adjacency ratio for each node. MAR[i] equals 1 if all non-zero adjacencies between node i and the remaining network nodes equal 1. This fundamental network concept is always 1 for nodes of an unweighted network. This is a useful measure for weighted networks since it allows one to determine whether a node has high connectivity because of many weak connections (small MAR) or because of strong (but few) connections (high MAR), see Horvath and Dong 2008.

Density

the density of the network.

Centralization

the centralization of the network.

Heterogeneity

the heterogeneity of the network.

Author(s)

Steve Horvath

References

Dong J, Horvath S (2007) Understanding Network Concepts in Modules, BMC Systems Biology 2007, 1:24

Horvath S, Dong J (2008) Geometric Interpretation of Gene Coexpression Network Analysis. PLoS Comput Biol 4(8): e1000117

See Also

conformityBasedNetworkConcepts for calculation of conformity based network concepts for a network adjacency matrix;

networkConcepts, for calculation of conformity based and eigennode based network concepts for a correlation network.