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We propose the concept of open network as an arbitrary selection of nodes of a large unknown network. Using the hypothesis that information of the whole network structure can be extrapolated from an arbitrary set of its nodes, we use Renyi…
Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same…
Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…
Network architecture design is very important for the optimization of industrial networks. The type of network architecture can be divided into small-scale network and large-scale network according to its scale. Graph theory is an efficient…
Complex network theory has been applied to solving practical problems from different domains. In this paper, we present a general framework for complex network applications. The keys of a successful application are a thorough understanding…
A substantial volume of research has been devoted to studies of community structure in networks, but communities are not the only possible form of large-scale network structure. Here we describe a broad extension of community structure that…
What is a complex network? How do we characterize complex networks? Which systems can be studied from a network approach? In this text, we motivate the use of complex networks to study and understand a broad panoply of systems, ranging from…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows…
We present a statistical mechanics approach for the description of complex networks. We first define an energy and an entropy associated to a degree distribution which have a geometrical interpretation. Next we evaluate the distribution…
Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
Network theory provides tools which are particularly appropriate for assessing the complex interdependencies that characterise our modern connected world. This article presents an introduction to network theory, in a way that doesn't…
Relations between discrete quantities such as people, genes, or streets can be described by networks, which consist of nodes that are connected by edges. Network analysis aims to identify important nodes in a network and to uncover…
Network models are used to study interconnected systems across many physical, biological, and social disciplines. Such models often assume a particular network-generating mechanism, which when fit to data produces estimates of…
This article discusses how concepts and methods of complex networks can be applied to real-time imaging and computer vision. After a brief introduction of complex networks basic concepts, their use as means to represent and characterize…
The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of information theory to networks. In this paper we…
The fundamental concept of applying the system methodology to network analysis declares that network architecture should take into account services and applications which this network provides and supports. This work introduces a formal…
Network analysis has a crucial need for tools to compare networks and assess the significance of differences between networks. We propose a principled statistical approach to network comparison that approximates networks as probability…