Life span in online communities.

Recently online communities have attracted great interest and have become an important medium of information exchange between users. The aim of this work is to introduce a simple model of the evolution of online communities. This model describes (a) the time evolution of users' activity in a web service, e.g., the time evolution of the number of online friends or written posts, (b) the time evolution of the degree distribution of a social network, and (c) the time evolution of the number of active users of a web service. In the second part of the paper we investigate the influence of the users' lifespan (i.e., the total time in which they are active in an online community) on the process of rumor propagation in evolving social networks. Viral marketing is an important application of such method of information propagation.

Dynamic phenomena and human activity in an artificial society.

We study dynamic phenomena in a large social network of nearly 3x10;{4} individuals who interact in the large virtual world of a massive multiplayer online role playing game. On the basis of a database received from the online game server, we examine the structure of the friendship network and human dynamics. To investigate the relation between networks of acquaintances in virtual and real worlds, we carried out a survey among the players. We show that, even though the virtual network did not develop as a growing graph of an underlying network of social acquaintances in the real world, it influences it. Furthermore we find very interesting scaling laws concerning human dynamics. Our research shows how long people are interested in a single task and how much time they devote to it. Surprisingly, exponent values in both cases are close to -1 . We calculate the activity of individuals, i.e., the relative time daily devoted to interactions with others in the artificial society. Our research shows that the distribution of activity is not uniform and is highly correlated with the degree of the node, and that such human activity has a significant influence on dynamic phenomena, e.g., epidemic spreading and rumor propagation, in complex networks. We find that spreading is accelerated (an epidemic) or decelerated (a rumor) as a result of superspreaders' various behavior.

Evolution of a social network: the role of cultural diversity.

We present a simple deterministic and based on local rules model of evolving social network, which leads to a network with the properties of a real social system, e.g., small-world topology and assortative mixing. The state of an individual Si is characterized by the values of Q cultural features, drawn from Gaussian distribution with variance sigma. The other control parameter is sociability Ti, which describes the maximal number of connections of an individual. The state of individuals and connections between them evolve in time. As results from numerical computations, an initial diversity of cultural features in a community has an essential influence on an evolution of social network. It was found that for a critical value of control parameter sigma c(Q) there is a structural transition and a hierarchical network with small-world topology of connections and a high clustering coefficient emerges. The emergence of small-world properties can be related to the creation of subculture groups in a community. The power-law relation between the clustering coefficient of a node and its connectivity C(k) approximately k-beta was observed in the case of a scale-free distribution of sociability Ti and a high enough cultural diversity in a population.

Epidemic spreading in a hierarchical social network.

A model of epidemic spreading in a population with a hierarchical structure of interpersonal interactions is described and investigated numerically. The structure of interpersonal connections is based on a scale-free network. Spatial localization of individuals belonging to different social groups, and the mobility of a contemporary community, as well as the effectiveness of different interpersonal interactions, are taken into account. Typical relations characterizing the spreading process, like a range of epidemic and epidemic curves, are discussed. The influence of preventive vaccinations on the spreading process is investigated. The critical value of preventively vaccinated individuals that is sufficient for the suppression of an epidemic is calculated. Our results are compared with solutions of the master equation for the spreading process and good agreement of the character of this process is found.