# Ego-betweenness Centrality

#### Definition

It takes into account the temporal information, it does not demand the knowledge of the global structure of the network, it is computationally light and parameter-free.

$$C(e,\tau)={\underset{i,j\in N_e \times N_e}{\sum}} {p_{ij}(e,\tau)\over p_{ij}(\tau)} ,$$

where $p_{ij}(\tau)$ is the number of most recent paths of length at most 2 from $i$ to $j$ at time $\tau$ and $p_{ij}(e,\tau)$ is the number of such paths going through $e$.

It only takes into account the direct neighbors of a node to compute its centrality. This restriction allows to carry out the computation in a shorter time compared to a case where any couple of nodes in the network should be considered.

$$C(e,\tau)={\underset{i,j\in N_e \times N_e}{\sum}} {p_{ij}(e,\tau)\over p_{ij}(\tau)} ,$$

where $p_{ij}(\tau)$ is the number of most recent paths of length at most 2 from $i$ to $j$ at time $\tau$ and $p_{ij}(e,\tau)$ is the number of such paths going through $e$.

It only takes into account the direct neighbors of a node to compute its centrality. This restriction allows to carry out the computation in a shorter time compared to a case where any couple of nodes in the network should be considered.

#### References

- Ghanem, M., Coriat, F. and Tabourier, L., 2017, July. Ego-betweenness centrality in link streams. In Proceedings of the 2017 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining 2017 (pp. 667-674). DOI: 10.1145/3110025.3110158