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Spatially-embedded complex networks, such as nervous systems, the Internet and transportation networks, generally have non-trivial topological patterns of connections combined with nearly minimal wiring costs. However the growth rules…

The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a…

We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the non-linear behaviour is different, the linearized set of coupled…

Unstoppable feedback loops and tipping points in socio-ecological systems are the main threats to sustainability. These behaviors have been extensively studied, notably to predict, and arguably deviate, dead-end trajectories. Behind the…

It is widely believed that the formation of brain network structure is under the pressure of optimal trade-off between reducing wiring cost and promoting communication efficiency. However, the question of whether this trade-off exists in…

Unlike many physical nonequilibrium systems, in biological systems, the coupling to external energy sources is not a fixed parameter but adaptively controlled by the system itself. We do not have theoretical frameworks that allow for such…

The structure of pipe networks minimizing the total energy dissipation rate is studied analytically. Among all the possible pipe networks that can be built with a given total pipe volume (or pipe lateral surface area), the network which…

In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under…

It was hypothesized that the structures of biological transport networks are the result of either energy consumption or adaptation dynamics. Although approaches based on these hypotheses can produce optimal network and form loop structures,…

We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…

We proposed an evolving network model constituted by the same nodes but different edges. The competition between nodes and different links were introduced. Scale free properties have been found in this model by continuum theory. Different…

The quest to understand structure-function relationships in networks across scientific disciplines has intensified. However, the optimal network architecture remains elusive, particularly for complex information processing. Therefore, we…

Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…

Supply chains are the backbone of the global economy. Disruptions to them can be costly. Centrally managed supply chains invest in ensuring their resilience. Decentralized supply chains, however, must rely upon the self-interest of their…

We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…

There has been a long debate on how new levels of organization have evolved. It might seem unlikely, as cooperation must prevail over competition. One well-studied example is the emergence of autocatalytic sets, which seem to be a…

We consider robustness and percolation properties of the networks of networks, in which random nodes in different individual networks (layers) can be interdependent. We explore the emergence of the giant mutually connected component,…

We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…

Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…

In this study, we performed comprehensive morphological investigations of the spontaneous formations of effective network structures among elements in coupled logistic maps, specifically with a delayed connection change. Our proposed model…