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Network Motif CentralityDefinition
Based on network motifs and principal component analysis (PCA), Network Motif Centrality measure
node importance in directed biological networks.
For a network with n nodes, the procedures of the proposed measure are as follows:
Endow each motif with a weight w_{j}, j= 1, 2,…,m, where w_{j}=c_{j}/Σ^{m}_{k=1}c_{k} here, c_{k}(k = 1, 2,…,m) denotes the number of the kth type of motif. Matrix B computed as B=(b_{ij})_{n×m} = (b1,b2,...,bm) = (w_{j}u_{ij})_{n×m} and Σ as covariance matrix of B. Based on B and the idea of the PCA, the following index defined to obtain node importance score: where α is eigenvector corresponding matrix Σ. SoftwareReferences
