Network Motif Centrality

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:

1. Detect 2, 3 and 4-node network motifs in the network.
2. Count the occurrences of each node in m types of motifs, and derive a n×m matrix A.
3. Perform data processing on A, such as weighting and standardizing matrix A, then we obtain a matrix B. Compute the covariance matrix Σ of B.
4. For Σ, compute the biggest eigenvalue λ and the corresponding unit eigenvector α.
5. Compute I^score and rank the n nodes accordingly.

Suppose A = (u_ij)_n×m as matrix for a directed network where n is nodes number, m is totally types of 2, 3 and 4 node motifs and u_ij is the occurrences of node i in the j-th type of motif (i= 1,…, n, j= 1,… m).
Endow each motif with a weight w_j, j= 1, 2,…,m, where w_j=c_j/Σ^m_k=1c_k here, c_k(k = 1, 2,…,m) denotes the number of the k-th type of motif.
Matrix B computed as B=(b_ij)_n×m = (b1,b2,...,bm) = (w_ju_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.

• WANG, P., LÜ, J. & YU, X. 2014. Identification of Important Nodes in Directed Biological Networks: A Network Motif Approach. PLoS ONE, 9, e106132. DOI: 10.1371/journal.pone.0106132
• WANG, P., YU, X. & LU, J. 2014. Identification and Evolution of Structurally Dominant Nodes in Protein-Protein Interaction Networks. Biomedical Circuits and Systems, IEEE Transactions on, 8, 87-97.