Viral Marketing Branching Processes

We consider the inherent timeline structure of the appearance of content in online social networks (OSNs) while studying content propagation. We model the propagation of a post/content of interest by an appropriate multi-type branching process. The branching process allows one to predict the emergence of global macro properties (e.g., the spread of a post in the network) from the laws and parameters that determine local interactions. The local interactions largely depend upon the timeline (an inverse stack capable of holding many posts and one dedicated to each user) structure and the number of friends (i.e., connections) of users, etc. We explore the use of multi-type branching processes to analyze the viral properties of the post, e.g., to derive the expected number of shares, the probability of virality of the content, etc. In OSNs, the new posts push down the existing contents in timelines, which can greatly influence content propagation; our analysis considers this influence. We find that one leads to draw incorrect conclusions when the timeline (TL) structure is ignored: (a) for instance, even less attractive posts are shown to get viral; (b) ignoring TL structure also indicates erroneous growth rates. More importantly, one cannot capture some interesting paradigm shifts/phase transitions; for example, virality chances are not monotone with network activity parameter, as shown by analysis including TL influence. In the last part, we integrate the online auctions into our viral marketing model. We study the optimization problem considering real-time bidding. We again compared the study with and without considering the TL structure for varying activity levels of the network. We find that the analysis without TL structure fails to capture the relevant phase transitions, thereby making the study incomplete.