Related papers: The spatial structure of networks
Air pollution can be studied in the urban structure regulated by transport networks. Transport networks can be studied as geometric and topological graph characteristics through designed models. Current studies do not offer a comprehensive…
Vibrant development of a network-based economy requires separating investment in highly location specific local access technology from the development of standardized, geography-independent, wide-area network services. Thus far…
Networks are widely used to represent interaction pattern among the components in complex systems. Structures of real networks from differ- ent domains may vary quite significantly. Since there is an interplay be- tween network architecture…
Social network structure is very important for understanding human information diffusing, cooperating and competing patterns. It can bring us with some deep insights about how people affect each other. As a part of complex networks, social…
A prominent model for transportation networks is branched transport, which seeks the optimal transportation scheme to move material from a given initial to a final distribution. The cost of the scheme encodes a higher transport efficiency…
We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely…
Interactions between units in phyical, biological, technological, and social systems usually give rise to intrincate networks with non-trivial structure, which critically affects the dynamics and properties of the system. The focus of most…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
We consider two variational models for transport networks, an urban planning and a branched transport model, in which the degree of network complexity and ramification is governed by a small parameter $\varepsilon>0$. Smaller $\varepsilon$…
Motivated by the shape of transportation networks such as subways, we consider a distribution of points in the plane and ask for the network $G$ of given length $L$ that is optimal in a certain sense. In the general model, the optimality…
Route diversity in networks is elemental for establishing reliable, high-capacity connections with appropriate security between endpoints. As for the Internet, route diversity has already been studied at both Autonomous System- and…
Complex networks are characterized by several topological properties: degree distribution, clustering coefficient, average shortest path length, etc. Using a simple model to generate scale-free networks embedded on geographical space, we…
To analyze the transport of information or material from a source to every node of a network we use two quantities introduced in the study of river networks: the cost and the flow. For a network with $K$ nodes and $M$ levels, we show that…
Economy, and consequently trade, is a fundamental part of human social organization which, until now, has not been studied within the network modelling framework. Networks are mathematical tools used in the modelling of a wide variety of…
The structure of real-world social networks in large part determines the evolution of social phenomena, including opinion formation, diffusion of information and influence, and the spread of disease. Globally, network structure is…
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…
The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…
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…
Web services growth makes the composition process a hard task to solve. This numerous interacting elements can be adequately represented by a network. Discovery and composition can benefit from the knowledge of the network structure. In…