| Summary: | It is of importance to model and estimate the user influence in social networks, especially for advertisers who conduct viral marketing. In this paper, we are interested in the number of received messages incurred by a node generating a message, and introduce the concepts of individual influence and type influence, while type influence is got by averaging out individual influence over nodes of the same type. We propose a user behavior model and use generating function to analyze type influence (including the mean and variance) and diffusion threshold, and find these results are not accurate in finite-size networks. We then classify nodes into subtypes and redefine the network model, which achieves much more accurate results. We also propose a scalable approach to estimate individual influence, and find it can get good approximates for individual influence, subtype influence and type influence by only considering local neighbors and out-of-date information, which is useful in large-scale networks. All analysis results are verified by simulations in real-world networks. Models in this paper can be extended to consider more realistic situations, and we believe these results are of use in understanding the diffusion dynamics in social networks.
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