Related papers: Topological identification in networks of dynamica…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
The discovery of small world and scale free properties of many real world networks has revolutionized the way we study, analyze, model and process networks. An important way to analyze these complex networks is to visualize them using graph…
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…
Distance plays a fundamental role in measuring similarity between objects. Various visualization techniques and learning tasks in statistics and machine learning such as shape matching, classification, dimension reduction and clustering…
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…
A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…
The network inference problem consists of reconstructing the edge set of a network given traces representing the chronology of infection times as epidemics spread through the network. This problem is a paradigmatic representative of…
Previous efforts in complex networks research focused mainly on the topological features of such networks, but now also encompass the dynamics. In this Letter we discuss the relationship between structure and dynamics, with an emphasis on…
This Letter presents a unified approach for the fundamental relationship between structure and function in flow networks by solving analytically the voltages in a resistor network, transforming the network structure to an effective…
Reconstructing weighted networks from partial information is necessary in many important circumstances, e.g. for a correct estimation of systemic risk. It has been shown that, in order to achieve an accurate reconstruction, it is crucial to…
Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…
The ability to reroute and control flow is vital to the function of venation networks across a wide range of organisms. By modifying individual edges in these networks, either by adjusting edge conductances or creating and destroying edges,…
In this paper we develop a theory to describe innovation processes in a network of interacting units. We introduce a stochastic picture that allows for the clarification of the role of fluctuations for the survival of innovations in such a…
Complex network theory provides a powerful framework to statistically investigate the topology of local and non-local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same…
We propose a topological framework for the detection of Hopf bifurcations directly from time series, based on persistent homology applied to phase space reconstructions via Takens embedding within the framework of Topological Data Analysis.…
This paper proposes a novel approach for detecting the topology of distribution networks based on the analysis of time series measurements. The time-based analysis approach draws on data from high-precision phasor measurement units (PMUs or…
We present a simple model of network dynamics that can be solved analytically for uniform networks. We obtain the dynamics of response of the system to perturbations. The analytical solution is an excellent approximation for random…
In this review, we give an introduction to the structural and functional properties of the biological networks. We focus on three major themes: topology of complex biological networks like the metabolic and protein-protein interaction…
Complex networks encountered in biology are often characterized by significant structural diversity. Whether it be differences in the three-dimensional structure of allosteric proteins, or the variation among the micro-scale structures of…
We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…