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Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…
Network theory has unveiled the underlying structure of complex systems such as the Internet or the biological networks in the cell. It has identified universal properties of complex networks, and the interplay between their structure and…
Recent research on the network modeling of complex systems has led to a convenient representation of numerous natural, social, and engineered systems that are now recognized as networks of interacting parts. Such systems can exhibit a…
Social interactions vary in time and appear to be driven by intrinsic mechanisms, which in turn shape the emerging structure of the social network. Large-scale empirical observations of social interaction structure have become possible only…
Networks represent relationships between entities in many complex systems, spanning from online social interactions to biological cell development and brain connectivity. In many cases, relationships between entities are unambiguously…
The district of southern California and Japan are divided into small cubic cells, each of which is regarded as a vertex of a graph if earthquakes occur therein. Two successive earthquakes define an edge and a loop, which replace the complex…
Scale-free (SF) networks and small world networks have been found to occur in very diverse contexts. It is this striking universality which makes one look for widely applicable mechanisms which lead to the formation of such networks. In…
Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order…
Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. {While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the…
Social networks are of interest to researchers in part because they are thought to mediate the flow of information in communities and organizations. Here we study the temporal dynamics of communication using on-line data, including e-mail…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
Various disasters stem from minor perturbations, such as the spread of infectious diseases, cascading failure in power grids, etc. Analyzing perturbations is crucial for both theoretical and application fields. Previous researchers have…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…
Many physical systems--from mechanical lattices and electrical circuits to biological tissues and architected metamaterials--can be understood as networks transmitting physical quantities. We present a unified mathematical framework for…
Graphs have often been used to answer questions about the interaction between real-world entities by taking advantage of their capacity to represent complex topologies. Complex networks are known to be graphs that capture such non-trivial…
The sun provides an explosive, heavenly example of self-organized criticality. Sudden bursts of intense radiation emanate from rapid rearrangements of the magnetic field network in the corona. Avalanches are triggered by loops of flux that…
Synchronization and resonance on networks are some of the most remarkable collective dynamical phenomena. The network topology, or the nature and distribution of the connections within an ensemble of coupled oscillators, plays a crucial…
Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the…
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…
Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks' structural characteristics, however, are rarely taken into account when studying their…