Modern social interaction is rapidly moving towards the virtual social networks. Computerized networking infrastructure enables us to monitor and analyze information spreading, innovation diffusion and opinion formation in social networks. This stimulates attempts for a deep understanding and modeling of networked social process.
There are two main approaches for modeling idea spreading. The infection approach assumes that in each contact between actors with some probability the opinion will spared on. The threshold approach assumes that the probability of opinion spreading dramatically increases when is reached a certain fraction of opinioned neighbors.
In both approaches mentioned above, there isn't a significant difference in the opinion spreading time by different actors as a starting point, which contradicts sociology theories according to which there are key actors in social environments, called influencers. For this reason we proposed a new model, which capture the main difference between information and opinion spreading.
In information spreading additional exposure to certain information has a small effect. Contrary, when an actor is exposed to 2 opinioned actors the probability to adopt the opinion is significant higher than in the case of contact with one such actor (called by J. Kleinberg "the 0-1-2 effect"). In each time step for each actor that does not have an opinion, we randomly choose 2 of his network neighbors. If one of them has an opinion, the actor obtains opinion with some low probability, if two – with a higher probability.
Opinion spreading was simulated on different real world social networks (network of e-mail contacts, network of scientific citation) and similar random scale-free networks. In each simulation we defined a starting actor (whom which will influence the network) and the number of actors with opinion by time line was measured. The behavior of the spreading is characterized by a slow incline, until reaching a critical point (or tipping point on time line, tp) after that the spreading speed is dramatically increasing. The simulation results show that after reaching tp the spreading in the network is independent on the starting actor, but the value of tp is strongly dependent on starting actor. The best influencer actor has a significant number of friends, however not all actors with large number of friends are good influencers.
Known characteristics of an actor in a network can not indicate if he is a potential influencer. It's clear that an influencer must not have a low degree and must have a high clustering coefficient value. To be an influencer a special position of actor in the network is needed and this position is not a local property of the actor. Further investigations will be concentrated on accurate definition of this position together with introducing of new topological metrics of a network.
