Active and passive diffusion processes in complex networks

Ideas, information, viruses: all of them, with their mechanisms, spread over the complex social information, viruses: all tissues described by our interpersonal relations. Usually, to simulate and understand the unfolding of such complex phenomena are used general mathematical models; these models act agnostically from the object of which they simulate the diffusion, thus considering spreading of virus, ideas and innovations alike. Indeed, such degree of abstraction makes it easier to define a standard set of tools that can be applied to heterogeneous contexts; however, it can also lead to biased, incorrect, simulation outcomes. In this work we introduce the concepts of active and passive diffusion to discriminate the degree in which individuals choice affect the overall spreading of content over a social graph. Moving from the analysis of a well-known passive diffusion schema, the Threshold model (that can be used to model peer-pressure related processes), we introduce two novel approaches whose aim is to provide active and mixed schemas applicable in the context of innovations/ideas diffusion simulation. Our analysis, performed both in synthetic and real-world data, underline that the adoption of exclusively passive/active models leads to conflicting results, thus highlighting the need of mixed approaches to capture the real complexity of the simulated system better.