Abstract
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approximates for individual influence, subtype influence and type influence by only considering local neighbors and out-of-date information, which is useful in large-scale networks.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.
Highlights
Social networks have drawn increasing attention from both research and industry communities [1]–[4], due to their important effects in facilitating information sharing among users
We introduce the concept of individual influence here, and define the individual influence uv as the number of messages which are received during the diffusion process, which is incurred by node v generating a message
We introduce the concept of type influence, and define the type influence ui as the number of messages which are received during the diffusion process, which is incurred by a type i node generating a message
Summary
Social networks have drawn increasing attention from both research and industry communities [1]–[4], due to their important effects in facilitating information sharing among users. It is of great importance to characterize the process of information diffusion, and model and estimate the user influence in social networks. The diffusion models widely used in the research of social networks are the Independent Cascade (IC) [17], [18] and Linear Threshold (LT) [19] models The former is sender-centered, and each active node influences its inactive neighbors independently with given probabilities. We use generating function to analyze the mean and variance of type influence as well as diffusion threshold, and find the results are not accurate in finite-size networks. We conduct simulations in real-world networks to verify the analysis results, and believe these results are of importance in understanding the process of information diffusion in social networks, and critical for an advertiser who wants to estimate a user’s influence before posting an advertisement
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