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Recently, research that focuses on the rigorous understanding of the relation between simulation and/or exact models on graphs and approximate counterparts has gained lots of momentum. This includes revisiting the performance of classic…
Social interactions are stratified in multiple contexts and are subject to complex temporal dynamics. The systematic study of these two features of social systems has started only very recently mainly thanks to the development of multiplex…
Higher order interactions are increasingly recognised as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraph as well as simplicial complexes capture the higher-order interactions of complex…
We introduce group-based compartmental modeling (GBCM), a mean-field framework for irreversible contagion in higher-order networks that captures structural heterogeneity and correlations across group sizes. Validated through numerical…
Designing algorithms that generate networks with a given degree sequence while varying both subgraph composition and distribution of subgraphs around nodes is an important but challenging research problem. Current algorithms lack control of…
Recent work has shown that different theoretical approaches to the dynamics of the Susceptible-Infected-Susceptible (SIS) model for epidemics lead to qualitatively different estimates for the position of the epidemic threshold in networks.…
At the cellular scale, biochemical processes are governed by random interactions between reactant molecules with small copy counts, leading to behavior that is inherently stochastic. Such systems are often modeled as continuous-time Markov…
Competition and collaboration are at the heart of multi-agent probabilistic spreading processes. The battle on public opinion and competitive marketing campaigns are typical examples of the former, while the joint spread of multiple…
Binary-state dynamics (such as the susceptible-infected-susceptible (SIS) model of disease spread, or Glauber spin dynamics) on random networks are accurately approximated using master equations. Standard mean-field and pairwise theories…
Herding is a deterministic algorithm used to generate data points that can be regarded as random samples satisfying input moment conditions. The algorithm is based on the complex behavior of a high-dimensional dynamical system and is…
In the semi-streaming model for processing massive graphs, an algorithm makes multiple passes over the edges of a given $n$-vertex graph and is tasked with computing the solution to a problem using $O(n \cdot \text{polylog}(n))$ space.…
The conventional design of real-time approaches depends heavily on the normal performance of systems and it often becomes incapacitated in dealing with catastrophic scenarios effectively. There are several investigations carried out to…
Epidemics in large complete networks is well established. In contrast, we consider epidemics in non-complete networks. We establish the fluid limit macroscopic dynamics of a multi-virus spread over a multipartite network as the number of…
It is in practice impossible to describe the topology of a real network or its message propagation process using a single dynamic model. To address this issue, we constructed a new hybrid network model based on scale-free (SF), small-world…
Hypergraphs offer flexible and robust data representations for many applications, but methods that work directly on hypergraphs are not readily available and tend to be prohibitively expensive. Much of the current analysis of hypergraphs…
Network science has evolved into an indispensable platform for studying complex systems. But recent research has identified limits of classical networks, where links connect pairs of nodes, to comprehensively describe group interactions.…
Models of epidemics over networks have become popular, as they describe the impact of individual behavior on infection spread. However, they come with high computational complexity, which constitutes a problem in case large-scale scenarios…
We present an algorithm for finding the probabilities of rare events in nonequilibrium processes. The algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently. By keeping track…
Hypergraphs, increasingly utilised to model complex and diverse relationships in modern networks, have gained significant attention for representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery…
Partitioning large networks into stable clusters of synchronized nodes is a challenging task. Recent approaches based on spectral analysis can provide exact results on specific dynamics but remain unfeasible for very large networks.…