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Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
Prediction and control of the dynamics of complex networks is a central problem in network science. Structural and dynamical similarities of different real networks suggest that some universal laws might accurately describe the dynamics of…
Dynamical processes on time-varying complex networks are key to understanding and modeling a broad variety of processes in socio-technical systems. Here we focus on empirical temporal networks of human proximity and we aim at understanding…
In this paper we consider nodes in network are heterogeneous and the link between nodes is caused by the potential dynamical demand of the nodes. Such demand can be measured by gravitation which increases with the heterogeneous strength of…
Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems…
Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly-connected groups…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
Empirical estimation of critical points at which complex systems abruptly flip from one state to another is among the remaining challenges in network science. However, due to the stochastic nature of critical transitions it is widely…
Since long back, scientists have been putting enormous effort to understand earthquake dynamics -the goal is to develop a successful prediction scheme which can provide reliable alarm that an earthquake is imminent. Model studies sometimes…
We understand the dynamics of the world around us as by associating pairs of events, where one event has some influence on the other. These pairs of events can be aggregated into a web of memories representing our understanding of an…
Earthquake occurrence in nature is thought to result from correlated elastic stresses, leading to clustering in space and time. We show that occurrence of major earthquakes in California correlates with time intervals when fluctuations in…
Extreme events have low occurrence probabilities and display pronounced deviation from their average behaviour, such as earthquakes or power blackouts. Such extreme events occurring on the nodes of a complex network have been extensively…
The connectivity of a network contains information about the relationships between nodes, which can denote interactions, associations, or dependencies. We show that this information can be analyzed by measuring the uncertainty (and…
Statistical tests of earthquake predictions require a null hypothesis to model occasional chance successes. To define and quantify `chance success' is knotty. Some null hypotheses ascribe chance to the Earth: Seismicity is modeled as…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
The collaboration network is an example of a social network which has both non-trivial temporal and spatial dependence. Based on the observations of collaborations in Physical Review Letters, a model of collaboration network is proposed…
The concept of emergence is a powerful concept to explain very complex behaviour by simple underling rules. Existing approaches of producing emergent collective behaviour have many limitations making them unable to account for the…
Post-earthquake hazard and impact estimation are critical for effective disaster response, yet current approaches face significant limitations. Traditional models employ fixed parameters regardless of geographical context, misrepresenting…
Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the…
Stars and cycles are basic structures in network construction. The former has been well studied in network analysis, while the latter attracted rare attention. A node together with its neighbors constitute a neighborhood star-structure…