Active and passive diffusion processes in complex networks

Milli et al. Applied Network Science (2018) 3:42 https://doi.org/10.1007/s41109-018-0100-5 Applied Network Science R ES EA R CH Open Access Active and passive diffusion processes in complex networks Letizia Milli1,2*† , Giulio Rossetti1,2† , Dino Pedreschi1 and Fosca Giannotti2 *Correspondence: † Letizia Milli and Giulio Rossetti contributed equally to this work. 1 University of Pisa, Largo B. Pontecorvo, 2, Pisa, Italy 2 KDD Lab. ISTI-CNR, via G. Moruzzi, 1, Pisa, Italy Abstract Ideas, 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. Keywords: Diffusion processes, Complex networks, Diffusion of information Introduction 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. Agents can be either individuals or animals as well as computers or other technological devices connected by a complex network describing their relations. 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 be passive and doomed to suffer a diffusion process (e.g., during an outbreak of influenza) or active and voluntarily adopt a given behavior or idea just because they feel it right. Moreover, agents can also 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. Indeed, such ambivalence is strictly tied to specific contents and contexts and can be modeled using different approaches. © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Milli et al. Applied Network Science (2018) 3:42 The activeness distinction regards prevalently phenomena of social contagion, where the diffusing object is either an idea or a piece of information. Social contagions are often modeled using a classical approach, the Threshold model (Granovetter 1978) introduced by Granovetter in 1978. In this model the adoption of ideas or information by an individual is subject to a personal threshold; these approaches, however, tend to capture only the passive component of the diffusion, ignoring the user interests concerning the information. However, peer pressure is not the only component that acts as the linchpin for individual’s adoption: personal interest plays a relevant role, an active impulse that - once the subject is aware of the existence of the content - disregarding the peer pressure volume can inhibit/facilitate the diffusive process. Indeed, 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. Moreover, in the real world exist some people that decide autonomously to adopt an idea or information without peer pressure from their friends and others that decide not to adopt that ideas. So in this work, we modeled also the spontaneous adoption phenomenon and the presence of blocked nodes. After having characterized active and passive diffusion schema, we tackle the problem of understanding if, and how, spontaneous adoption and blocked nodes affect the diffusion of innovations/ideas. Indeed, a plethora of diffusion models can be designed to capture such behaviors - some of them even interchangeably, assigning different semantics to the variables they expose. To overcome such issue, in this work we decided to perform a simple distinction: we model passive approaches through deterministic diffusion rules (i.e., individual thresholds that mimic peer-pressure phenomena) and active ones through probabilistic ones (i.e., individual profiles that depends only on the interest of the subject into the diffusing content). The paper is organized as follows. In Section “Related works” are introduced and discussed related works on diffusion process modeling. In Section “Social diffusion conundrum” we formalize our problem definition, characterizing the different diffusion scenarios we will analyze, namely active, passive and mixed diffusion. There we also introduce the algorithmic schema we used to simulate such scenarios. In Section “Experimental analysis” we approach the analytical part of our investigation: there the datasets, methodology and experimental results – for all the identified scenarios and network settings – are introduced and discussed. Finally, Section “Conclusion” concludes the paper. Related works Generally, diffusion processes can be roughly broken down into three components: (i) the population on which they unfold, (ii) the mechanisms that describe their evolution, and (iii) the content of the diffusion. All those components are equally important to model, understand, simulate a diffusion process: in particular, the content spread represents the real discriminant among active/passive diffusion. Commonly, the phrase “epidemic spreading” is used to imply the diffusion of contagious diseases caused by biological pathogens, like influenza, measles, chickenpox as well as sexually transmitted diseases. However, a plethora of phenomena can be linked to the (...truncated)