Related papers: Geometry of Complex Networks and Topological Centr…
This paper addresses the problem of identifying the graph structure of a dynamical network using measured input/output data. This problem is known as topology identification and has received considerable attention in recent literature. Most…
We introduce and use k-shell decomposition to investigate the topology of the Internet at the AS level. Our analysis separates the Internet into three sub-components: (a) a nucleus which is a small (~100 nodes) very well connected globally…
We solve the problem of identifying (reconstructing) network topology from steady state network measurements. Concretely, given only a data matrix $\mathbf{X}$ where the $X_{ij}$ entry corresponds to flow in edge $i$ in configuration…
Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…
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…
Robust and comprehensive characterization of the topological properties of complex networks requires the adoption of several respective measurements, among which the node degree has special importance. In the present work, we provide an…
Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut core-periphery dichotomy.…
Metric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes…
At the core of understanding dynamical systems is the ability to maintain and control the systems behavior that includes notions of robustness, heterogeneity, or regime-shift detection. Recently, to explore such functional properties, a…
The geometric renormalization technique for complex networks has successfully revealed the multiscale self-similarity of real network topologies and can be applied to generate replicas at different length scales. In this letter, we extend…
Metric networks are network-shaped, one-dimensional structures on which one can solve differential equations to simulate a wide range of physical systems including conjugated molecules, photonic crystals, quantum mechanics in waveguide…
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…
Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…
This article examines the inverse problem for a lossy quantum graph that is internally excited and sensed. In particular, we supply an algorithmic methodology for deducing the topology and geometric structure of the underlying metric graph.…
We consider the problem of recovering the topology and the edge conductance value, as well as characterizing a set of electrical networks that satisfy the limitedly available Thevenin impedance measurements. The measurements are obtained…
This paper develops a unified framework for measuring concentration in weighted systems embedded in networks of interactions. While traditional indices such as the Herfindahl-Hirschman Index capture dispersion in weights, they neglect the…
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,…
The understanding of the immense and intricate topological structure of the World Wide Web (WWW) is a major scientific and technological challenge. This has been tackled recently by characterizing the properties of its representative graphs…
Mapping the Internet generally consists in sampling the network from a limited set of sources by using traceroute-like probes. This methodology, akin to the merging of different spanning trees to a set of destination, has been argued to…
Though commonly found in the real world, directed networks have received relatively less attention from the literature in which concerns their topological and dynamical characteristics. In this work, we develop a magnetic Laplacian-based…