Abstract
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.
Highlights
Information, ideas, viruses all of them have something in common: they describe different kinds of “contents” that need to be vehiculated by interacting agents to diffuse
The active-passive dichotomy have not yet been adequately addressed nor formal models considering active users in network diffusion proposed: for this reason in this study we describe variants of the threshold model aimed to start filling such gap
From compartmental models (e.g., SI, SIR, SIS) the Threshold model once given an initial infection status produces a deterministic evolution of the diffusion: the lack of a stochastic component, along with the model rationale, makes the diffusion produced by the observed model passive, i.e., a process during which the nodes involved do not play any active role
Summary
Information, ideas, viruses all of them have something in common: they describe different kinds of “contents” that need to be vehiculated by interacting agents to diffuse. Even if similar at a high abstraction level, diffusion process have their characteristics that profoundly affect the way they evolve. One such characteristic is undoubtedly tied to the degree of activeness of the agents they aimed to reach. Agents can show both of such behaviors: in some circumstances a content can need both a certain degree of exposure of actors as well as their interest to be adopted. Such ambivalence is strictly tied to specific contents and contexts and can be modeled using different approaches
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