Evolving Bipartite Model Reveals the Bounded Weights in Mobile Social Networks


Users and items in recommendation networks, authors and scientific topics in scholarly networks, male and female in dating social networks, and so on are all examples of real-world mobile social networks that can be described as evolving bipartite graphs. These graphs show how dynamically added elements are split into two entities and connected by links between these two entities. However, despite the fact that connections between two entities are frequently weighted, the mathematical modeling of such weighted evolving bipartite relationships, along with their quantitative characterizations, is still an area that has not been sufficiently investigated. This serves as the impetus for the development of a novel evolving bipartite model (EBM), which reveals, on the basis of an empirically validated power-law distribution on multiple realistic mobile social networks, that the distribution of total weights of incoming and outgoing edges in networks is determined by the weighting scale and is bounded by certain ceilings and floors. This was accomplished by developing a novel evolving bipartite model (EBM), which was motivated by the aforementioned. On the basis of these theoretical findings, EBM is able to make predictions regarding the overall weights of vertices in evolving bipartite networks whose degree distributions follow power-laws. To provide an illustration, in recommendation networks, the evaluation of items, also known as total rating scores, can be estimated through the given bounds; in scholarly networks, the total number of publications under specific topics can be anticipated within a certain range; and in dating social networks, the favorability of male or female can be roughly measured. Finally, we perform extensive experiments on 10 realistic datasets and a synthetic network with varying weights, also known as rating scales, in order to further evaluate the performance of EBM. The experimental results demonstrate that, given weighting scales, both the upper bound and the lower bound of total weights of vertices in mobile social networks can be accurately predicted by the EBM. This is important because the upper bound represents the maximum amount of total weight that a vertex can have, while the lower bound represents the minimum amount of

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