# Reciprocity

The reciprocity metric determines the level of bi-directional interactions between users. Its value is calculated from dividing the in-degree by the out-degree as suggested by Viol et al. (2016).

Smith et al. (2009) and Angeletou et al. (2011) propose the same idea, but divide the in-degree by the count of replying authors or the total degree, respectively.

I propose to use the definition from Angeletou et al. (2011) as it describes the metric accurately and its values are normalised in the range from zero to one. This metric is calculated for individuals and therefore it is of ego-centric scope.

The calculation for the reciprocity $r$ is as follows:

1. select count of posts where the given user is the targt
2. select count of posts where the given user is the source or target
3. r := count of received posts / total posts


Alternatively the calculation of the reciprocity $r$ can be done via the graph measures in-degree and total degree: $$r = \frac{d_{in}(v_i)}{d_{in}(v_i) + d_{out}(v_i)}$$

Viol et al. (2016) relate a high reciprocity to power users, who are active and engage with other users in the network on a regular basis. They contribute by driving discussions and spawning threads with novel ideas and knowledge (Smith et al., 2009).

A high reciprocity improves community activity and interactions between users (Angeletou et al., 2011). It is important that users contribute with a high intensity and regularity over a longer period of time. Preferably, they are active in all parts of the network, so it is densely connected. The dense connectedness and high engagement is a sign of Bonding Social Capital in the network.

Reciprocal interactions are an indicator for strong social ties and Bonding Social Capital. It enables effective collaboration based on trust and a shared understanding. This teamwork can improve a network's performance according to Burt et al. (2001).