Section: New Results

Modeling of Dynamics of Complex Networks

Participants : Jean Pierre Chevrot, Christophe Crespelle, Sicheng Dai, Éric Fleury, Eric, Philippe Guichard, Márton Karsai, Yannick Leo, Sebastien Lerique, Jacob Levy Abitbol, Jean-Philippe Magué, Matteo Morini, Samuel Unicomb, Samuel Unicomb.

Multilayer networks

In [67] we introduce a new class of stochastic multilayer networks. A stochastic multilayer network is the aggregation of $M$ networks (one per layer) where each is a subgraph of a foundational network $G$. Each layer network is the result of probabilistically removing links and nodes from $G$. The resulting network includes any link that appears in at least $K$ layers. This model is an instance of a non-standard site-bond percolation model. Two sets of results are obtained: first, we derive the probability distribution that the $M$-layer network is in a given configuration for some particular graph structures (explicit results are provided for a line, an algorithm is provided for a tree), where a configuration is the collective state of all links (each either active or inactive). Next, we show that for appropriate scalings of the node and link selection processes in a layer, links are asymptotically independent as the number of layers goes to infinity, and follow a Poisson distribution. Numerical results are provided to highlight the impact of having several layers on some metrics of interest (including expected size of the cluster a node belongs to in the case of the line). This model finds applications in wireless communication networks with multichannel radios, multiple social networks with overlapping memberships, transportation networks, and, more generally, in any scenario where a common set of nodes can be linked via co-existing means of connectivity.

Models of time varying networks

In terms of modelling temporal networks we had the following main contributions in 2017.

A book on Bursty Human Dynamics, written by M. Karsai as a the leading author. Bursty dynamics is a common temporal property of various complex systems in Nature but it also characterises the dynamics of human actions and interactions. At the phenomenological level it is a feature of all systems that evolve heterogeneously over time by alternating between periods of low and high event frequencies. In such systems, bursts are identified as periods in which the events occur with a rapid pace within a short time-interval while these periods are separated by long periods of time with low frequency of events. As such dynamical patterns occur in a wide range of natural phenomena, their observation, characterisation, and modelling have been a long standing challenge in several fields of research. However, due to some recent developments in communication and data collection techniques it has become possible to follow digital traces of actions and interactions of humans from the individual up to the societal level. This led to several new observations of bursty phenomena in the new but largely unexplored area of human dynamics, which called for the renaissance to study these systems using research concepts and methodologies, including data analytics and modelling. As a result, large amount of new insight and knowledge as well as innovations have been accumulated in the field, which provided the timely opportunity to write a monograph book [56] to make an up-to-date review and summary of the observations, appropriate measures, modelling, and applications of heterogeneous bursty patterns occurring in the dynamics of human behaviour.

In another contribution M. Karsai and collaborators introduced a new representation of temporal networks [73]. The dynamics of diffusion-like processes on temporal networks are influenced by correlations in the times of contacts. This influence is particularly strong for processes where the spreading agent has a limited lifetime at nodes: disease spreading (recovery time), diffusion of rumors (lifetime of information), and passenger routing (maximum acceptable time between transfers). We introduce weighted event graphs as a powerful and fast framework for studying connectivity determined by time-respecting paths where the allowed waiting times between contacts have an upper limit. We study percolation on the weighted event graphs and in the underlying temporal networks, with simulated and real-world networks. We show that this type of temporal-network percolation is analogous to directed percolation, and that it can be characterized by multiple order parameters.

M. Karsai also contributed to a new definition to better quantify attention distributed in dynamical egocentric social networks [64]. Granovetter's weak tie theory of social networks is built around two central hypotheses. The first states that strong social ties carry the large majority of interaction events; the second maintains that weak social ties, although less active, are often relevant for the exchange of especially important information (e.g., about potential new jobs in Granovetter's work). While several empirical studies have provided support for the first hypothesis, the second has been the object of far less scrutiny. A possible reason is that it involves notions relative to the nature and importance of the information that are hard to quantify and measure, especially in large scale studies. Here, we search for empirical validation of both Granovetter's hypotheses. We find clear empirical support for the first. We also provide empirical evidence and a quantitative interpretation for the second. We show that attention, measured as the fraction of interactions devoted to a particular social connection, is high on weak ties — possibly reflecting the postulated informational purposes of such ties — but also on very strong ties. Data from online social media and mobile communication reveal network-dependent mixtures of these two effects on the basis of a platform's typical usage. Our results establish a clear relationships between attention, importance, and strength of social links, and could lead to improved algorithms to prioritize social media content.

Dynamical processes on networks

Another field which has been intensively studied during the last year addresses dynamical processes on temporal and static networks.

In a book chapter M. Karsai summarised his recent findings on temporal network immunisation [57]. The vast majority of strategies aimed at controlling contagion processes on networks consider a timescale separation between the evolution of the system and the unfolding of the process. However, in the real world, many networks are highly dynamical and evolve, in time, concurrently to the contagion phenomena. Here, we review the most commonly used immunization strategies on networks. In the first part of the chapter, we focus on controlling strategies in the limit of timescale separation. In the second part instead, we introduce results and methods that relax this approximation. In doing so, we summarize the main findings considering both numerical and analytically approaches in real as well as synthetic time-varying networks.

With the PhD student S. Unicomb, M. Karsai and a collaborator developed a new formalism, which is capable to precisely capture and predict the non-monotonous dependence of threshold driven dynamics on weight heterogeneities in networks [76]. Weighted networks capture the structure of complex systems where interaction strength is meaningful. This information is essential to a large number of processes, such as threshold dynamics, where link weights reflect the amount of influence that neighbours have in determining a node's behaviour. Despite describing numerous cascading phenomena, such as neural firing or social contagion, the modelling of threshold dynamics on weighted networks has been largely overlooked. We fill this gap by studying a dynamical threshold model over synthetic and real weighted networks with numerical and analytical tools. We show that the time of cascade emergence depends non-monotonously on weight heterogeneities, which accelerate or decelerate the dynamics, and lead to non-trivial parameter spaces for various networks and weight distributions. Our methodology applies to arbitrary binary state processes and link properties, and may prove instrumental in understanding the role of edge heterogeneities in various natural and social phenomena.

With other co-authors, M. Karsai published another book chapter about his recent findings on the modelling threshold driven dynamics on networks [55]. The collective behaviour of people adopting an innovation, product or online service is commonly interpreted as a spreading phenomenon throughout the fabric of society. This process is arguably driven by social influence, social learning and by external effects like media. Observations of such processes date back to the seminal studies by Rogers and Bass, and their mathematical modelling has taken two directions: One paradigm, called simple contagion, identifies adoption spreading with an epidemic process. The other one, named complex contagion, is concerned with behavioural thresholds and successfully explains the emergence of large cascades of adoption resulting in a rapid spreading often seen in empirical data. The observation of real world adoption processes has become easier lately due to the availability of large digital social network and behavioural datasets. This has allowed simultaneous study of network structures and dynamics of online service adoption, shedding light on the mechanisms and external effects that influence the temporal evolution of behavioural or innovation adoption. These advancements have induced the development of more realistic models of social spreading phenomena, which in turn have provided remarkably good predictions of various empirical adoption processes. In this chapter we review recent data-driven studies addressing real-world service adoption processes. Our studies provide the first detailed empirical evidence of a heterogeneous threshold distribution in adoption. We also describe the modelling of such phenomena with formal methods and data-driven simulations. Our objective is to understand the effects of identified social mechanisms on service adoption spreading, and to provide potential new directions and open questions for future research.

Y. Leo, E. Fleury and M. Karsai is in the final stage to publish a study on a unique mobile call/banking dataset on the dynamics of purchasing patterns. We analyse a coupled dataset collecting the mobile phone communications and bank transactions history of a large number of individuals living in a Latin American country. After mapping the social structure and introducing indicators of socioeconomic status, demographic features, and purchasing habits of individuals we show that typical consumption patterns are strongly correlated with identified socioeconomic classes leading to patterns of stratification in the social structure. In addition we measure correlations between merchant categories and introduce a correlation network, which emerges with a meaningful community structure. We detect multivariate relations between merchant categories and show correlations in purchasing habits of individuals. Finally, by analysing individual consumption histories, we detect dynamical patterns in purchase behaviour and their correlations with the socioeconomic status, demographic characters and the egocentric social network of individuals. Our work provides novel and detailed insight into the relations between social and consuming behaviour with potential applications in resource allocation, marketing, and recommendation system design.

SoSweet

The SoSweet project focuses on the synchronic variation and the diachronic evolution of the variety of French language used on Twitter.

In one paper accepted to WWW'18 we addressed some of the main questions of the project using a unique dataset combining the largest French Twitter dataset and demographic data coming from INSEE [31]. Our usage of language is not solely reliant on cognition but is arguably determined by myriad external factors leading to a global variability of linguistic patterns. This issue, which lies at the core of sociolinguistics and is backed by many small-scale studies on face-to-face communication, is addressed here by constructing a dataset combining the largest French Twitter corpus to date with detailed socioeconomic maps obtained from national census in France. We show how key linguistic variables measured in individual Twitter streams depend on factors like socioeconomic status, location, time, and the social network of individuals. We found that (i) people of higher socioeconomic status, active to a greater degree during the daytime, use a more standard language; (ii) the southern part of the country is more prone to use more standard language than the northern one, while locally the used variety or dialect is determined by the spatial distribution of socioeconomic status; and (iii) individuals connected in the social network are closer linguistically than disconnected ones, even after the effects of status homophily have been removed. Our results inform sociolinguistic theory and may inspire novel learning methods enabling the inference of socioeconomic status of people from the way they tweet.

Relational methods for media studies

A very relevant application of the research that DANTE carries out on networks structures and networks dynamics concerns the field of journalism and media study. Relational analysis may be helpful in these fields in two different way.

On the one hand, the advent of digital media has challenged the established vertical structure of information distribution typical of broadcasting media with a decentralised organisation that facilitates the spreading of contents through all sort of horizontal channels (in the Web and in Social Media). This new type of circulation is still insufficiently studied and require both quantitative and qualitative investigation. We tried to provide the first in our Field Guide to Fake News already introduced in the highlights of this document [68] and in a forthcoming chapter on the heterogeneous clustering of French Media system for the The Routledge Handbook to Developments in Digital Journalism Studies [60]. As for the qualitative study of the structure of the media system, we published and analysis of the strategies employed by Facebook to steer the evolution of the technology of Live Video Streaming [23].

On the other hand, network analysis can be a powerful tool to investigate and narrate journalistic stories, but its techniques need adapted to the language used by journalists and understood by their audiences. We tried to provide such a translation in a paper for the journal Digital Journalism [13] and in a chapter for the Datafied Society book [59].

The use of network analysis to study vast societal phenomena has also profound implications for the theory of social sciences, which we tried to explore in a paper for the journal Big Data & Society [25] and in a chapter of a book on the Frontiers of Social Science [63], and for their practice [62].

Philosophy of technologies revisited by Internet

The Internet, as a technology of writing, helps us to understand that a technology is not always a mean to reach a goal, nor an application of science. In fact, the Internet does not appear as a revolution, but as a revealer. We understand that a technology can be reflexive (it invites us to think it) and that it cannot be clearly separated from human activities (writing, etc.). For instance, 50 years ago, we imagined we could think with our own mind (and perhaps with a paper and pencil). Now, we know that we cannot think without material stuff (a computer, the internet, etc.). A very few philosophers knew this fact (Leibniz, Boole, etc.). But this evidence transforms completely the philosophy of technologies. Another important point is the effect of technology on epistemology. We realise that we can not ask or imagine some questions if the technology is not there (eg: social cartography or statistics). This fact invites us to insert technologies and methods in the traditional diptych of theory and experience. In synthesis, we also discover strong links between technology and culture; hence the role of engineers in the construction of culture [53], [18], [52], [54], [71].