The role of degree correlation in shaping filter bubbles in social networks

Filter bubbles shelter people from unconcerned but important information, which is a critical problem in modern online social networks. Although a quantitative model of filter bubbles is still missing, the identification and impact of filter bubbles are widely debated both at a scientific and political level. To shed light on this gap, we introduce a theoretical directed network model of filter bubbles with degree correlations and mathematically analyze information diffusion dynamics on the model. We find that the internal structure of filter bubbles can be modeled by the directed scale-free network with both negative (a node tend to possess high in-degree and low out-degree, or vice versa) and assortative (two nodes with similar degrees tend to be connected) degree correlation. Traditionally, filter bubbles are usually associated with the community structure and emphasize the sparseness of external connections to isolate the spreading of diverse information. However, the negative-assortative degree correlation shows that the filter bubble can spontaneously resist the spreading of non-preferred information (i.e., information with relatively lower transmissibility). Moreover, we study the competition epidemic of two information on the negative-assortative networks, and find that both of the information can coexist only if all nodes prefer the same information.