arXiv subjects

Marton Karsai

Publications and source records attributed to Marton Karsai.

8 recordsLinked to original sources

arXiv2026

Universal time scales linking topology and dynamics in temporal networks

Temporal networks underlie a wide range of social, technological, and biological phenomena, highlighting how temporal inhomogeneities drive interactions in complex systems. Despite vast research on the area, the way temporal network connectivity evolves across time scales remains poorly understood. By analyzing temporal network data of informational and societal origin, involving tens of systems, millions of nodes, and observation periods from days to years, we find systematic evidence of an optimal time scale for coarse-graining interaction events. At this level of aggregation, networks are maximally dynamic in their local structure, while retaining system-wide connectivity. To understand the origins of such a seemingly generic interplay of time and topology, we explore a minimal temporal network model based on uncorrelated renewal processes, and show that intermittent yet globally connected activity may arise solely due to heterogeneities in inter-event times and degrees, and no other system-specific details. All coarse-grained empirical networks studied show persistent patterns of cyclic node degree change yet stationary system-level degree distributions, a striking coexistence of microscopic self-regulation and macroscopic stability. Our results give support to the notion of a universal pattern in temporal networks that involves both time and topology, via the nontrivial interplay of aggregation and temporal inhomogeneity, with consequences for the study of spreading dynamics on networks and the balance between robustness and adaptability in complex systems.

physics.soc-ph↗

arXiv2024

Human Mobility in the Metaverse

The metaverse promises a shift in the way humans interact with each other, and with their digital and physical environments. The lack of geographical boundaries and travel costs in the metaverse prompts us to ask if the fundamental laws that govern human mobility in the physical world apply. We collected data on avatar movements, along with their network mobility extracted from NFT purchases. We find that despite the absence of commuting costs, an individuals inclination to explore new locations diminishes over time, limiting movement to a small fraction of the metaverse. We also find a lack of correlation between land prices and visitation, a deviation from the patterns characterizing the physical world. Finally, we identify the scaling laws that characterize meta mobility and show that we need to add preferential selection to the existing models to explain quantitative patterns of metaverse mobility. Our ability to predict the characteristics of the emerging meta mobility network implies that the laws governing human mobility are rooted in fundamental patterns of human dynamics, rather than the nature of space and cost of movement.

cs.SI↗

arXiv2023

Generalized contact matrices for epidemic modeling

Contact matrices have become a key ingredient of modern epidemic models. They account for the stratification of contacts for the age of individuals and, in some cases, the context of their interactions. However, age and context are not the only factors shaping contact structures and affecting the spreading of infectious diseases. Socio-economic status (SES) variables such as wealth, ethnicity, and education play a major role as well. Here, we introduce generalized contact matrices capable of stratifying contacts across any number of dimensions including any SES variable. We derive an analytical expression for the basic reproductive number of an infectious disease unfolding on a population characterized by such generalized contact matrices. Our results, on both synthetic and real data, show that disregarding higher levels of stratification might lead to the under-estimation of the reproductive number and to a mis-estimation of the global epidemic dynamics. Furthermore, including generalized contact matrices allows for more expressive epidemic models able to capture heterogeneities in behaviours such as different levels of adoption of non-pharmaceutical interventions across different groups. Overall, our work contributes to the literature attempting to bring socio-economic, as well as other dimensions, to the forefront of epidemic modeling. Tackling this issue is crucial for developing more precise descriptions of epidemics, and thus to design better strategies to contain them.

physics.soc-ph↗

arXiv2016

Burstiness and tie reinforcement in time varying social networks

We introduce a time-varying network model accounting for burstiness and tie reinforcement observed in social networks. The analytical solution indicates a non-trivial phase diagram determined by the competition of the leading terms of the two processes. We test our results against numerical simulations, and compare the analytical predictions with an empirical dataset finding good agreements between them. The presented framework can be used to classify the dynamical features of real social networks and to gather new insights about the effects of social dynamics on ongoing spreading processes.

physics.soc-ph↗

arXiv2015

Kinetics of Social Contagion

Diffusion of information, behavioral patterns or innovations follows diverse pathways depending on a number of conditions, including the structure of the underlying social network, the sensitivity to peer pressure and the influence of media. Here we study analytically and by simulations a general model that incorporates threshold mechanism capturing sensitivity to peer pressure, the effect of `immune' nodes who never adopt, and a perpetual flow of external information. While any constant, non-zero rate of dynamically-introduced spontaneous adopters leads to global spreading, the kinetics by which the asymptotic state is approached shows rich behavior. In particular we find that, as a function of the immune node density, there is a transition from fast to slow spreading governed by entirely different mechanisms. This transition happens below the percolation threshold of network fragmentation, and has its origin in the competition between cascading behavior induced by adopters and blocking due to immune nodes. This change is accompanied by a percolation transition of the induced clusters.

physics.soc-ph↗

arXiv2015

Detecting global bridges in networks

The identification of nodes occupying important positions in a network structure is crucial for the understanding of the associated real-world system. Usually, betweenness centrality is used to evaluate a node capacity to connect different graph regions. However, we argue here that this measure is not adapted for that task, as it gives equal weight to "local" centers (i.e. nodes of high degree central to a single region) and to "global" bridges, which connect different communities. This distinction is important as the roles of such nodes are different in terms of the local and global organisation of the network structure. In this paper we propose a decomposition of betweenness centrality into two terms, one highlighting the local contributions and the other the global ones. We call the latter bridgeness centrality and show that it is capable to specifically spot out global bridges. In addition, we introduce an effective algorithmic implementation of this measure and demonstrate its capability to identify global bridges in air transportation and scientific collaboration networks.

cs.SI↗

arXiv2013

Controlling Contagion Processes in Time-Varying Networks

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

physics.soc-ph↗

arXiv2011

Communities and beyond: mesoscopic analysis of a large social network with complementary methods

Community detection methods have so far been tested mostly on small empirical networks and on synthetic benchmarks. Much less is known about their performance on large real-world networks, which nonetheless are a significant target for application. We analyze the performance of three state-of-the-art community detection methods by using them to identify communities in a large social network constructed from mobile phone call records. We find that all methods detect communities that are meaningful in some respects but fall short in others, and that there often is a hierarchical relationship between communities detected by different methods. Our results suggest that community detection methods could be useful in studying the general mesoscale structure of networks, as opposed to only trying to identify dense structures.

physics.soc-ph↗