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## Section: New Results

### Computational Human Dynamics and Temporal Networks

Participants : Márton Karsai, Éric Fleury, Jean-Philippe Magué, Philippe Nain, Jean-Pierre Chevrot.

#### Correlations and dynamics of consumption patterns in social-economic networks

In [16], 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 [16]. 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.

#### Mapping temporal-network percolation to weighted, static event graphs

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). In [14], 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.

#### Randomized reference models for temporal networks

Many real-world dynamical systems can successfully be analyzed using the temporal network formalism. Empirical temporal networks and dynamic processes that take place in these situations show heterogeneous, non-Markovian, and intrinsically correlated dynamics, making their analysis particularly challenging. Randomized reference models (RRMs) for temporal networks constitute a versatile toolbox for studying such systems. Defined as ensembles of random networks with given features constrained to match those of an input (empirical) network, they may be used to identify statistically significant motifs in empirical temporal networks (i.e. overrepresented w.r.t. the null random networks) and to infer the effects of such motifs on dynamical processes unfolding in the network. However, the effects of most randomization procedures on temporal network characteristics remain poorly understood, rendering their use non-trivial and susceptible to misinterpretation. In the work presented in [52], we propose a unified framework for classifying and understanding microcanonical RRMs (MRRMs). We use this framework to propose a canonical naming convention for existing randomization procedures, classify them, and deduce their effects on a range of important temporal network features. We furthermore show that certain classes of compatible MRRMs may be applied in sequential composition to generate more than a hundred new MRRMs from existing ones surveyed in this article. We provide a tutorial for the use of MRRMs to analyze an empirical temporal network and we review applications of MRRMs found in literature. The taxonomy of MRRMs we have developed provides a reference to ease the use of MRRMs, and the theoretical foundations laid here may further serve as a base for the development of a principled and systematic way to generate and apply randomized reference null models for the study of temporal networks.

#### Socioeconomic dependencies of linguistic patterns in Twitter: a multivariate analysis

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 in [29], 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 for the inference of socioeconomic status of people from the way they tweet.

#### Threshold driven contagion on weighted networks

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 in [21], 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.

#### Link transmission centrality in large-scale social networks

Understanding the importance of links in transmitting information in a network can provide ways to hinder or postpone ongoing dynamical phenomena like the spreading of epidemic or the diffusion of information. In our work [22], we propose a new measure based on stochastic diffusion processes, thetransmission centrality, that captures the importance of links by estimating the average number of nodes to whom they transfer information during a global spreading diffusion process. We propose a simple algorithmic solution to compute transmission centrality and to approximate it in very large networks at low computational cost. Finally we apply transmission centrality in the identification of weak ties in three large empirical social networks, showing that this metric outperforms other centrality measures in identifying links that drive spreading processes in a social network.

#### Prepaid or Postpaid? That Is the Question: Novel Methods of Subscription Type Prediction in Mobile Phone Services

In the paper [41], we investigate the behavioural differences between mobile phone customers with prepaid and postpaid subscriptions. Our study reveals that (a) postpaid customers are more active in terms of service usage and (b) there are strong structural correlations in the mobile phone call network as connections between customers of the same subscription type are much more frequent than those between customers of different subscription types. Based on these observations, we provide methods to detect the subscription type of customers by using information about their personal call statistics, and also their egocentric networks simultaneously. The key of our first approach is to cast this classification problem as a problem of graph labelling, which can be solved by max-flow min-cut algorithms. Our experiments show that, by using both user attributes and relationships, the proposed graph labelling approach is able to achieve a classification accuracy of $\sim 87%$, which outperforms by $\sim 7%$ supervised learning methods using only user attributes. In our second problem, we aim to infer the subscription type of customers of external operators. We propose via approximate methods to solve this problem by using node attributes, and a two-way indirect inference method based on observed homophilic structural correlations. Our results have straightforward applications in behavioural prediction and personal marketing.