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Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…
The emergence of large-scale connectivity underlies the proper functioning of many networked systems, ranging from social networks and technological infrastructure to global trade networks. Percolation theory characterizes network formation…
We consider an alternate definition of community structure that is functionally motivated. We define network community structure-based on the function the network system is intended to perform. In particular, as a specific example of this…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular…
How spiking neuronal networks encode memories in their different time and spatial scales constitute a fundamental topic in neuroscience and neuro-inspired engineering. Much attention has been paid to large networks and long-term memory, for…
The brain is a paradigmatic example of a complex system as its functionality emerges as a global property of local mesoscopic and microscopic interactions. Complex network theory allows to elicit the functional architecture of the brain in…
Many systems such as critical infrastructure exhibit a modular structure with many links within the modules and few links between them. One approach to increase the robustness of these systems is to reinforce a fraction of the nodes in each…
Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of…
The brain is a highly complex organ consisting of a myriad of subsystems that flexibly interact and adapt over time and context to enable perception, cognition, and behavior. Understanding the multi-scale nature of the brain, i.e., how…
Semantic memory is the subsystem of human memory that stores knowledge of concepts or meanings, as opposed to life specific experiences. The organization of concepts within semantic memory can be understood as a semantic network, where the…
Modular structure is ubiquitous among complex networks. We note that most such systems are subject to multiple structural and functional constraints, e.g., minimizing the average path length and the total number of links, while maximizing…
Recent work in cognitive neuroscience has focused on analyzing the brain as a network, rather than as a collection of independent regions. Prior studies taking this approach have found that individual differences in the degree of modularity…
Network science plays an increasingly important role to model complex data in many scientific disciplines. One notable feature of network organization is community structure, which refers to clusters of tightly interconnected nodes. A…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…
Real-world networks are often organized as modules or communities of similar nodes that serve as functional units. These networks are also rich in content, with nodes having distinguishing features or attributes. In order to discover a…
Deep learning has seen a movement away from representing examples with a monolithic hidden state towards a richly structured state. For example, Transformers segment by position, and object-centric architectures decompose images into…
Measuring and optimizing the influence of nodes in big-data online social networks are important for many practical applications, such as the viral marketing and the adoption of new products. As the viral spreading on social network is a…
Brain network is remarkably cost-efficient while the fundamental physical and dynamical mechanisms underlying its economical optimization in network structure and activity are not clear. Here we study intricate cost-efficient interplay…