# DS - Dynamic-Sensitive Centrality

#### Definition

This method locating influential nodes of complex networks by integrating topological features and dynamical properties. Where the term dynamics-sensitive emphasizes the fact that $S(t)$ is determined not only by the network structure (i.e., $A$), but also the dynamical parameters (i.e., $β$ and $t$).

$$S_i(t)=m_1q_{1i}{\underset{j=1}{\overset{n}{\sum}}}q_{1j}+{\underset{r=2}{\overset{n}{\sum}}} m_r q_{ri} {\underset{j=1}{\overset{n}{\sum}}} q-{rj}$$

Were $T$ is time step, $m$ is infected neighbors, $q-i$ and $q_j$ are the eigenvector of the eigenvalue $\lambda_i$ and $\lambda_j$.

The main goal of this method is to find out the ranking of spreading influences of nodes, namely to identify influential nodes.

$$S_i(t)=m_1q_{1i}{\underset{j=1}{\overset{n}{\sum}}}q_{1j}+{\underset{r=2}{\overset{n}{\sum}}} m_r q_{ri} {\underset{j=1}{\overset{n}{\sum}}} q-{rj}$$

Were $T$ is time step, $m$ is infected neighbors, $q-i$ and $q_j$ are the eigenvector of the eigenvalue $\lambda_i$ and $\lambda_j$.

The main goal of this method is to find out the ranking of spreading influences of nodes, namely to identify influential nodes.

#### References

- Liu J., Lin J., Guo Q., Zhou T., 2016. Locating influential nodes via dynamics-sensitive centrality. Scientific Reports, 6. DOI: 10.1038/srep21380