# Distributed Current-Flow Betweenness Centrality

#### Definition

In this method the DUCKWEED , a distributed approach to calculate the current ﬂow betweenness centrality is applied

The current-ﬂow betweenness centrality $b_i$ is the average of the current ﬂows over all the source-target pairs:

$$b_i={{\sum_ {s < t} I_i^{s,t}}\over {(1/ 2)}n(n-1)}$$

$s$ is the source of the ﬂow, the current enters the network through it, $t$ is the target of the ﬂow, the current leaves the network through it, $I_i^{s,t}$ is current ﬂows. And the $b_i$ is the average of the current ﬂows over all the source-target pairs.

DUCKWEED delivers good results also for large graphs over millions of nodes, while previous approaches considered only thousands of nodes, and is characterized by a good scalability.

The current-ﬂow betweenness centrality $b_i$ is the average of the current ﬂows over all the source-target pairs:

$$b_i={{\sum_ {s < t} I_i^{s,t}}\over {(1/ 2)}n(n-1)}$$

$s$ is the source of the ﬂow, the current enters the network through it, $t$ is the target of the ﬂow, the current leaves the network through it, $I_i^{s,t}$ is current ﬂows. And the $b_i$ is the average of the current ﬂows over all the source-target pairs.

DUCKWEED delivers good results also for large graphs over millions of nodes, while previous approaches considered only thousands of nodes, and is characterized by a good scalability.

#### References

- Lulli A., Ricci L., Carlini E., Dazzi P., 2015. Distributed Current Flow Betweenness Centrality. International Conference on Self-Adaptive and Self-Organizing Systems, SASO, 2015-October, pp.71-80. DOI: 10.1109/SASO.2015.15