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Temporal hypergraphs capture time-resolved group interactions among nodes. Empirical data support that time-stamped group interactions show bursty event sequences and non-trivial temporal correlations. In the present study, we introduce…
A temporal random geometric graph is a random geometric graph in which all edges are endowed with a uniformly random time-stamp, representing the time of interaction between vertices. In such graphs, paths with increasing time stamps…
Temporal graphs represent the dynamic relationships among entities and occur in many real life application like social networks, e commerce, communication, road networks, biological systems, and many more. They necessitate research beyond…
In this note we establish a resilience version of the classical hitting time result of Bollob\'{a}s and Thomason regarding connectivity. A graph $G$ is said to be $\alpha$-resilient with respect to a monotone increasing graph property…
Empirical contact networks or interaction networks demonstrate peculiar characteristics stemming from the fundamental social, psychological, physical mechanisms governing human interactions. Although these mechanisms are complex, we test…
Random graphs with power-law degrees can model scale-free networks as sparse topologies with strong degree heterogeneity. Mathematical analysis of such random graphs proved successful in explaining scale-free network properties such as…
Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously…
Network epidemiology's most important assumption is that the contact structure over which infectious diseases propagate can be represented as a static network. However, contacts are highly dynamic, changing at many time scales. In this…
We introduce and simulate a growth model of the world-wide Web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real Web to update outgoing links (re)directing them towards constantly changing…
There is proposed a model of scale-free random graphs which are locally close to the uncorrelated complex random networks with divergent $\langle k^2 \rangle$ studied in e.g. S. N. Dorogovtsev {\it et al}, Rev. Mod. Phys. {\bf 80}, 1275…
How do networks of relationships evolve over time? We analyse a dataset tracking the social interactions of 900 individuals over four years. Despite continuous shifts in individual relationships, the macroscopic structural properties of the…
Power law distribution seems to be an important characteristic of web graphs. Several existing web graph models generate power law graphs by adding new vertices and non-uniform edge connectivities to existing graphs. Researchers have…
We analyze random networks that change over time. First we analyze a dynamic Erdos-Renyi model, whose edges change over time. We describe its stationary distribution, its convergence thereto, and the SI contact process on the network, which…
Many complex systems involve direct interactions among more than two entities and can be represented by hypergraphs, in which hyperedges encode higher-order interactions among an arbitrary number of nodes. To analyze structures and dynamics…
We consider the contact process on a random graph with fixed degree distribution given by a power law. We follow the work of Chatterjee and Durrett, who showed that for arbitrarily small infection parameter $\lambda$, the survival time of…
A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges. The network structure,…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
We develop a method to calculate the persistent currents and their spatial distribution (and transport properties) on graphs made of quasi-1D diffusive wires. They are directly related to the field derivatives of the determinant of a matrix…
One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…
Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…