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Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…

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…

Recent results from statistical physics show that large classes of complex networks, both man-made and of natural origin, are characterized by high clustering properties yet strikingly short path lengths between pairs of nodes. This class…

This paper introduces a new class of efficient inter connection networks called as M-graphs for large multi-processor systems.The concept of M-matrix and M-graph is an extension of Mn-matrices and Mn-graphs.We analyze these M-graphs…

We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…

Complex networks structures have been extensively used for describing complex natural and technological systems, like the Internet or social networks. More recently complex network theory has been applied to quantum systems, where complex…

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…

Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and…

A family of graphs optimized as the topologies for supercomputer interconnection networks is proposed. The special needs of such network topologies, minimal diameter and mean path length, are met by special constructions of the weight…

Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and…

In the last decade it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks: separable elements, with connections (or interactions) between certain pairs of them.…

The topology of classical networks is determined by physical links between nodes, and after a network request the links are used to establish the desired connections. Quantum networks offer the possibility to generate different kinds of…

Transportation and distribution networks are a class of spatial networks that have been of interest in recent years. These networks are often characterized by the presence of complex structures such as central loops paired with peripheral…

Constantly growing demands of high productivity and security of computer systems and computer networks call the interest of specialists in the environment of construction of optimum topologies of computer mediums. In earliest phases of…

Congruence theory has many applications in physical, social, biological and technological systems. Congruence arithmetic has been a fundamental tool for data security and computer algebra. However, much less attention was devoted to the…

Distributed computing has become a common practice nowadays, where the recent focus has been given to the usage of smart networking devices with in-network computing capabilities. State-of-the-art switches with near-line rate computing and…

The topology of any complex system is key to understanding its structure and function. Fundamentally, algebraic topology guarantees that any system represented by a network can be understood through its closed paths. The length of each path…

In decentralized optimization, nodes cooperate to minimize an overall objective function that is the sum (or average) of per-node private objective functions. Algorithms interleave local computations with communication among all or a subset…

We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…

The increasing demands in security and reliability of infrastructures call for the optimal design of their embedded complex networks topologies. The following question then arises: what is the optimal layout to fulfill best all the demands?…