Márton Karsai

Small But Slow World: How Network Topology and Burstiness Slow Down Spreading

While communication networks show the small-world property of short paths, the spreading dynamics in them turns out slow. Here, the time evolution of information propagation is followed through communication networks by using empirical data on contact sequences and the susceptible-infected model. Introducing null models where event sequences are appropriately shuffled, we are able to distinguish between the contributions of different impeding effects. The slowing down of spreading is found to be caused mainly by weight-topology correlations and the bursty activity patterns of individuals.

Universal features of correlated bursty behaviour

Inhomogeneous temporal processes, like those appearing in human communications, neuron spike trains, and seismic signals, consist of high-activity bursty intervals alternating with long low-activity periods. In recent studies such bursty behavior has been characterized by a fat-tailed inter-event time distribution, while temporal correlations were measured by the autocorrelation function. However, these characteristic functions are not capable to fully characterize temporally correlated heterogenous behavior. Here we show that the distribution of the number of events in a bursty period serves as a good indicator of the dependencies, leading to the universal observation of power-law distribution for a broad class of phenomena. We find that the correlations in these quite different systems can be commonly interpreted by memory effects and described by a simple phenomenological model, which displays temporal behavior qualitatively similar to that in real systems.

Circadian pattern and burstiness in mobile phone communication

The temporal communication patterns of human individuals are known to be inhomogeneous or bursty, which is reflected as heavy tail behavior in the inter-event time distribution. As the cause of such a bursty behavior two main mechanisms have been suggested: (i) inhomogeneities due to the circadian and weekly activity patterns and (ii) inhomogeneities rooted in human task execution behavior. In this paper, we investigate the role of these mechanisms by developing and then applying systematic de-seasoning methods to remove the circadian and weekly patterns from the time series of mobile phone communication events of individuals. We find that the heavy tails in the inter-event time distributions remain robust with respect to this procedure, which clearly indicates that the human task execution-based mechanism is a possible cause of the remaining burstiness in temporal mobile phone communication patterns.

Temporal motifs in time-dependent networks

Temporal networks are commonly used to represent systems where connections between elements are active only for restricted periods of time, such as telecommunication, neural signal processing, biochemical reaction and human social interaction networks. We introduce the framework of temporal motifs to study the mesoscale topological–temporal structure of temporal networks in which the events of nodes do not overlap in time. Temporal motifs are classes of similar event sequences, where the similarity refers not only to topology but also to the temporal order of the events. We provide a mapping from event sequences to coloured directed graphs that enables an efficient algorithm for identifying temporal motifs. We discuss some aspects of temporal motifs, including causality and null models, and present basic statistics of temporal motifs in a large mobile call network.

Controlling Contagion Processes in Activity Driven Networks

The vast majority of strategies aimed at controlling contagion processes on networks consider the connectivity pattern of the system either quenched or annealed. However, in the real world, many networks are highly dynamical and evolve, in time, concurrently with the contagion process. Here, we derive an analytical framework for the study of control strategies specifically devised for a class of time-varying networks, namely activity-driven networks. We develop a block variable mean-field approach that allows the derivation of the equations describing the coevolution of the contagion process and the network dynamic. We derive the critical immunization threshold and assess the effectiveness of three different control strategies. Finally, we validate the theoretical picture by simulating numerically the spreading process and control strategies in both synthetic networks and a large-scale, real-world, mobile telephone call data set.

Multiscale analysis of spreading in a large communication network

In temporal networks, both the topology of the underlying network and the timings of interaction events can be crucial in determining how a dynamic process mediated by the network unfolds. We have explored the limiting case of the speed of spreading in the SI model, set up such that an event between an infectious and a susceptible individual always transmits the infection. The speed of this process sets an upper bound for the speed of any dynamic process that is mediated through the interaction events of the network. With the help of temporal networks derived from large-scale time-stamped data on mobile phone calls, we extend earlier results that indicate the slowing-down effects of burstiness and temporal inhomogeneities. In such networks, links are not permanently active, but dynamic processes are mediated by recurrent events taking place on the links at specific points in time. We perform a multiscale analysis and pinpoint the importance of the timings of event sequences on individual links, their correlations with neighboring sequences, and the temporal pathways taken by the network-scale spreading process. This is achieved by studying empirically and analytically different characteristic relay times of links, relevant to the respective scales, and a set of temporal reference models that allow for removing selected time-domain correlations one by one. Our analysis shows that for the spreading velocity, time-domain inhomogeneities are as important as the network topology, which indicates the need to take time-domain information into account when studying spreading dynamics. In particular, results for the different characteristic relay times underline the importance of the burstiness of individual links.

Collective attention in the age of (mis)information

Display Omitted How 2.3 Facebook users consumed different information.Qualitatively different information is consumed in a similar way.Users more prone to interact with false claims are usually exposed to conspiracy rumors. In this work we study, on a sample of 2.3million individuals, how Facebook users consumed different information at the edge of political discussion and news during the last Italian electoral competition. Pages are categorized, according to their topics and the communities of interests they pertain to, in (a) alternative information sources (diffusing topics that are neglected by science and main stream media); (b) online political activism; and (c) main stream media. We show that attention patterns are similar despite the different qualitative nature of the information, meaning that unsubstantiated claims (mainly conspiracy theories) reverberate for as long as other information. Finally, we classify users according to their interaction patterns among the different topics and measure how they responded to the injection of 2788 false information. Our analysis reveals that users which are prominently interacting with conspiracists information sources are more prone to interact with intentional false claims.

Correlated Dynamics in Egocentric Communication Networks

We investigate the communication sequences of millions of people through two different channels and analyse the fine grained temporal structure of correlated event trains induced by single individuals. By focusing on correlations between the heterogeneous dynamics and the topology of egocentric networks we find that the bursty trains usually evolve for pairs of individuals rather than for the ego and his/her several neighbours, thus burstiness is a property of the links rather than of the nodes. We compare the directional balance of calls and short messages within bursty trains to the average on the actual link and show that for the trains of voice calls the imbalance is significantly enhanced, while for short messages the balance within the trains increases. These effects can be partly traced back to the technological constraints (for short messages) and partly to the human behavioural features (voice calls). We define a model that is able to reproduce the empirical results and may help us to understand better the mechanisms driving technology mediated human communication dynamics.

Complex contagion process in spreading of online innovation

Diffusion of innovation can be interpreted as a social spreading phenomenon governed by the impact of media and social interactions. Although these mechanisms have been identified by quantitative theories, their role and relative importance are not entirely understood, as empirical verification has so far been hindered by the lack of appropriate data. Here we analyse a dataset recording the spreading dynamics of the worlds largest Voice over Internet Protocol service to empirically support the assumptions behind models of social contagion. We show that the rate of spontaneous service adoption is constant, the probability of adoption via social influence is linearly proportional to the fraction of adopting neighbours, and the rate of service termination is time-invariant and independent of the behaviour of peers. By implementing the detected diffusion mechanisms into a dynamical agent-based model, we are able to emulate the adoption dynamics of the service in several countries worldwide. This approach enables us to make medium-term predictions of service adoption and disclose dependencies between the dynamics of innovation spreading and the socio-economic development of a country.

Entropy of dynamical social networks

Human dynamical social networks encode information and are highly adaptive. To characterize the information encoded in the fast dynamics of social interactions, here we introduce the entropy of dynamical social networks. By analysing a large dataset of phone-call interactions we show evidence that the dynamical social network has an entropy that depends on the time of the day in a typical week-day. Moreover we show evidence for adaptability of human social behavior showing data on duration of phone-call interactions that significantly deviates from the statistics of duration of face-to-face interactions. This adaptability of behavior corresponds to a different information content of the dynamics of social human interactions. We quantify this information by the use of the entropy of dynamical networks on realistic models of social interactions.