The second system under investigation is LastFM – a music community server or, to be more precise, its part known as the Audioscrobbler project which was launched in 2002. Like in the other systems discussed here, there is one server connected to the Internet, on which user accounts are registered. There are about 1 × 10⁶ users of this system. Its special plug-in, an important part of the system, is installed into a music player application (e.g., winamp) It sends information about every song played by users to the Audioscrobbler server. Data thus gathered are used to find users with similar music tastes: people with similar tastes in music and who listen to the same songs are presented and recommended to users who can see this information on their personalized website via a web browser. People with similar taste in music can meet one another and make friends (mutual consent is required) and/or gather in groups (according to music genre, favorite performers, etc.). The users’ activity can be calculated eg. by the number of songs played over time.

The third system described in this paper is a booklovers’ system Shelfari. Shelfari is a website server similar to LastFm. Users can create accounts obtaining in this way their personalized website where they can create virtual shelves with books which they enjoy. The system recommends users to one another according to similar tastes and books read, it shows other people’s opinions about various books, and makes it possible to create or join groups.

The fourth system under investigation is XFire. It is a gamers’ community program similar to Internet chat systems integrated with almost all popular computer games. People who are playing a game do not need to quit it to chat with people who are doing something else at that moment because XFire makes it possible to talk inside games via a special chat window. People who like to play computer games use this application to maintain contact with other players even when they are not playing any game or are playing two games at the same time. XFire gives each user their own web space with their statistics (i.e., overall time played, list of friends). Information about overall playing time can be considered an indicator of human activity.

Online communities offer a great opportunity to investigate human dynamics, because so much information about individuals is registered in databases. To analyze to what extent people are interested in using a web-service over time, we studied the creation date and the last login date registered in a database. The lifespan of an individual T_L is defined as the number of days from the time the individual was added to the database (i.e., a user account was created) to the date of the last logging in, i.e., to the last activity of the user in the system. It should be noted that such definition of a lifespan makes it possible to eliminate the influence of users who drop out of the system.

We have shown that users’ behavior in different social systems does not differ much: the distributions of parameters describing users’ activity x in the system have the form
of the power law. The value of an exponent depends on the type of activity. Similar behavior is observed in the activity of individual agents in online auctions (the distribution of the total number of bids placed by the same agent follows the form of the power law), in the activity of 24 × 10⁷ users of the Microsoft Messenger instantmessaging system (the number of logins per user follows the form of the power law) and in the number of posts per blog (the data set of 45×10³ blogs was analyzed). We have investigated the relationship between x and time. In none of the systems did the power-law relationship have values of exponents greater than one. This indicates that in most cases users lose interest in their activity in online systems over time and become less and less active. The power-law form of distributions and time development of users in the systems under investigation and other results indicate that such a scaling law is common in human dynamics and should be taken into account in models of the evolution of social systems and of human activity. Moreover, it was recently found that the heavy-tailed distribution of the intercontact times between susceptible and infected individuals has a significant influence on the spreading of computer viruses. We suggest that our results concerning human behavior can have a significant influence on the dynamic phenomena in complex networks (e.g., rumor propagation or opinion formation).

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1. Dynamic phenomena and human activity in artificial society