#### User Activity over Time

With the metric temporal concentration of creating messages, Hacker et al. (2015) and Viol et al. (2016) propose the idea to look at when messages are created and how the user activity changes over time.

Angeletou et al. (2011) describe a similar metric called the churn rate, which is the loss of active users over time. I adopt the former definition as it is a good indicator for a user's activity. If the activity reaches 0, it can be concluded that this user is lost, which fits the latter metric.

The activity can be measured for single users and therefore is of ego-centric scope. An average can be calculated for the network and be interpreted in a global scope.

For the calculation of the user activity over time $ua$, the timestamps of the messages are aggregated on per-month basis. The term "YYYYMM" means the year and month of the given date. The result is a set of key-value pairs, where the key is the month and the value is the count of posts for that month.

1. select all messages from a given user
2. group the messages by date in the form of "YYYYMM"
3. ua := count the number of messages per month


Viol et al. (2016) state that a high and continuous level of engagement characterises a power user. They contribute actively and are well connected within the network. Due to their high activity, they have a short response time and react quickly to questions and new ideas. As they are well connected, they have a high visibility and can influence the opinions of the network. Holtzblatt et al. (2013) call this type of users active contributors.

The users are well connected within the network with a diverse set of other users. It can be assumed that such a user has strong relationships with a subset of these other users. Since it is difficult to maintain strong relationships, it can also be assumed that such a user has acquired weak relationships. In this sense the user is associated with the creation of Bridging and Bonding Social Capital for the network. The user's weak ties provide him with new information on a regular basis while the user can actively engage and collaborate with his strongly tied contacts.

A low activity can indicate a niche expert, who is only active in his group or an information seeker. The latter type of user tends to ask questions and passively consume information, but the user is lacking interactions with other users. Therefore the user is not well connected in the network. However, the former type can be well connected to other people of his topical interest. Such a user possesses strong relationships with his peers and through that is thought to establish Bonding Social Capital.

Berger et al. (2014) claim that a high user activity is a strong indicator of a healthy community. This is confirmed by Angeletou et al. (2011), who call it community popularity. It characterises a network, in which users engage with high intensity and motivate others users to contribute. If the activity in the network declines, it poses a serious threat to the health of the network as a whole. Therefore Angeletou et al. (2011) recommend community managers to act in case the activity drops.

Hacker et al. (2015) note that a high temporal concentration of activity indicates low engagement. Instead it is preferable to have continuous activity over time, leading to consistent engagement with the Enterprise Social Network. Hacker et al. (2015) state that this indicates a brokering position in a network according to the structural holes theory. Thus, it measures Bridging Social Capital.

Due to the measurement of both Bonding and Bridging Social Capital, this metric is relevant for finding the optimum performance of a group (Burt et al., 2001). It should be noted that power users are rarely found in a social network and thus other types of users prevail (Viol et al., 2016).