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Symmetries are fundamental to dynamical processes in complex networks such as cluster synchronization, which have attracted a great deal of current research. Finding symmetric nodes in large complex networks, however, has relied on…
In the last years, a remarkable theoretical effort has been made in order to understand stability and complexity in ecological communities. The non-random structures of real ecological interaction networks has been recognized as one key…
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…
The increasing interest in complex networks research has been a consequence of several intrinsic features of this area, such as the generality of the approach to represent and model virtually any discrete system, and the incorporation of…
We survey and introduce concepts and tools located at the intersection of information theory and network biology. We show that Shannon's information entropy, compressibility and algorithmic complexity quantify different local and global…
Measuring the vulnerability of communities in complex network has become an important topic in the research of complex system. Numerous existing vulnerability measures have been proposed to solve such problems, however, most of these…
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 -…
A majority of real life networks are weighted and sparse. The present article aims at characterization of weighted networks based on sparsity, as a measure of inherent diversity, of different network parameters. It utilizes sparsity index…
The identification of important nodes in complex networks is an area of exciting growth due to its applications across various disciplines like disease controlling, community finding, data mining, network system controlling, just to name a…
Many foraging microorganisms rely upon cellular transport networks to deliver nutrients, fluid and organelles between different parts of the organism. Networked organisms ranging from filamentous fungi to slime molds demonstrate a…
The increasing volume of ecologically and biologically relevant data has revealed a wide collection of emergent patterns in living systems. Analyzing different datasets, ranging from metabolic gene-regulatory to species interaction…
We introduce a new topological descriptor of a network called the density decomposition which is a partition of the nodes of a network into regions of uniform density. The decomposition we define is unique in the sense that a given network…
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…
When analyzing the statistical and topological characteristics of complex networks, an effective and convenient way is to compute the centralities for recognizing influential and significant nodes or structures, yet most of them are…
This paper is Part I of a two-part series devoting to the study of systematic measures in a complex biological network modeled by a system of ordinary differential equations. As the mathematical complement to our previous work [31] with…
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include Internet, WWW, a network of chemicals linked by chemical reactions, social relationship networks, citation networks, etc. The…
Spatial road networks have been widely employed to model the structure and connectivity of cities. In such representation, the question of spatial scale of the entities in the network, i.e. what its nodes and edges actually embody in…
Nestedness characterizes the linkage pattern of networked systems, indicating the likelihood that a node is linked to the nodes linked to the nodes with larger degrees than it. Networks of mutualistic relationship between distinct groups of…
Systems composed of distinct complex networks are present in many real-world environments, from society to ecological systems. In the present paper, we propose a network model obtained as a consequence of interactions between two species…
A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here,…