# IDEC - Infection Diffusion Eigenvector Centrality

#### Definition

This method derived from the analysis of the SIS model on networks from spectral point of view. IDEC considers all eigenvalues and corresponding eigenvectors. IDEC shows high predictability when the effective infection ratio is below the critical point.

$$C_{IDE,i}\equiv {\underset{k=1}{\overset{N}{\sum}}} exp(\beta \lambda_k - \delta) u_{ki}||u_k||$$

where $N$ denotes the number of nodes in the network, $u_{ki}$ denotes the $i$th element of the eigenvector of the $k$th eigenvalue and the norm $||u_k||$ denotes the sum of all elements of the $k$th eigenvector. $\beta$ is infection probability and $\delta$ is recovery probability.

IDEC shows better predictability to find the vulnerable node(s) for the SIS model in the real networks than that of the existing centrality measures, such as degree centrality, eigenvector centrality, and Alpha-centrality.

$$C_{IDE,i}\equiv {\underset{k=1}{\overset{N}{\sum}}} exp(\beta \lambda_k - \delta) u_{ki}||u_k||$$

where $N$ denotes the number of nodes in the network, $u_{ki}$ denotes the $i$th element of the eigenvector of the $k$th eigenvalue and the norm $||u_k||$ denotes the sum of all elements of the $k$th eigenvector. $\beta$ is infection probability and $\delta$ is recovery probability.

IDEC shows better predictability to find the vulnerable node(s) for the SIS model in the real networks than that of the existing centrality measures, such as degree centrality, eigenvector centrality, and Alpha-centrality.