# Network Motif Centrality

#### Definition

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

Matrix B computed as B=(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.

For a network with n nodes, the procedures of the proposed measure are as follows:

- Detect 2, 3 and 4-node network motifs in the network.
- Count the occurrences of each node in m types of motifs, and derive a n×m matrix A.
- 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.
- For Σ, compute the biggest eigenvalue λ and the corresponding unit eigenvector α.
- Compute I
^{score}and rank the n nodes accordingly.

_{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=1}c_{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_{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.

#### Software

#### References

- 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.