# WSL-EC - Weighted Sum of Loads Eigenvector Centrality

#### Definition

The weighted sum of loads eigenvector centrality $(WSL-EC)$ counting all eigenvectors with a different and more simple weighting strategy in order to capture topologically important nodes not only from the densely populated but from the less densely populated and peripheral parts of the human network.

$$WSL-EC_i={\sum}_{j=1}^N |\lambda_j|.|v_{ij}|$$

Where, $N$ is the number of nodes in the network, $\lambda_j$ is the $j$th eigenvalue of the adjacency matrix and $v_{ij}$ is the load of $i$th node to the $j$th principal of the graph spectra.

The performance of $WSL-EC$ in the identification of topologically important nodes that contribute to the integrity of network and to capture biologically central nodes were tested in a human global protein-protein interaction network and it outperforms other centrality metrics in detecting biologically central nodes.

$$WSL-EC_i={\sum}_{j=1}^N |\lambda_j|.|v_{ij}|$$

Where, $N$ is the number of nodes in the network, $\lambda_j$ is the $j$th eigenvalue of the adjacency matrix and $v_{ij}$ is the load of $i$th node to the $j$th principal of the graph spectra.

The performance of $WSL-EC$ in the identification of topologically important nodes that contribute to the integrity of network and to capture biologically central nodes were tested in a human global protein-protein interaction network and it outperforms other centrality metrics in detecting biologically central nodes.

#### References

- Karabekmez M., Kirdar B., 2016. A novel topological centrality measure capturing biologically important proteins. Molecular BioSystems, 12(2), pp.666-673. DOI: 10.1039/C5MB00732A