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Information of localization properties of eigenvectors of the complex network has applicability in many different areas which include networks centrality measures, spectral partitioning, development of approximation algorithms, and disease…
We study localization properties of principal eigenvector (PEV) of multilayer networks. Starting with a multilayer network corresponding to a delocalized PEV, we rewire the network edges using an optimization technique such that the PEV of…
Understanding the localization properties of eigenvectors of complex networks is important to get insight into various structural and dynamical properties of the corresponding systems. Here, we analytically develop a scheme to construct a…
Investigation of eigenvector localization properties of complex networks is not only important for gaining insight into fundamental network problems such as network centrality measure, spectral partitioning, development of approximation…
The spectral properties of the adjacency matrix, in particular its largest eigenvalue and the associated principal eigenvector, dominate many structural and dynamical properties of complex networks. Here we focus on the localization…
Complex networks or graphs provide a powerful framework to understand importance of individuals and their interactions in real-world complex systems. Several graph theoretical measures have been introduced to access importance of the…
The quest to understand structure-function relationships in networks across scientific disciplines has intensified. However, the optimal network architecture remains elusive, particularly for complex information processing. Therefore, we…
We study spectra of directed networks with inhibitory and excitatory couplings. We investigate in particular eigenvector localization properties of various model networks for different value of correlation among their entries. Spectra of…
The spectral properties of the adjacency matrix provide a trove of information about the structure and function of complex networks. In particular, the largest eigenvalue and its associated principal eigenvector are crucial in the…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…
The mathematical framework of multiplex networks has been increasingly realized as a more suitable framework for modelling real-world complex systems. In this work, we investigate the optimization of synchronizability in multiplex networks…
We show that eigenvector centrality exhibits localization phenomena on networks that can be easily partitioned by the removal of a vertex cut set, the most extreme example being networks with a cut vertex. Three distinct types of…
We analyze gene co-expression network under the random matrix theory framework. The nearest neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral…
Network embedding, which aims to learn low-dimensional representations of nodes, has been used for various graph related tasks including visualization, link prediction and node classification. Most existing embedding methods rely solely on…
An important feature of many complex systems, both natural and artificial, is the structure and organization of their interaction networks with interesting properties. Here we present a theory of self-organization by evolutionary adaptation…
Optimization for deep networks is currently a very active area of research. As neural networks become deeper, the ability in manually optimizing the network becomes harder. Mini-batch normalization, identification of effective respective…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
We consider the problem of optimally allocating resources across a set of transmitters and receivers in a wireless network. The resulting optimization problem takes the form of constrained statistical learning, in which solutions can be…
The effects of link rewiring are considered for the class of directed networks where each node has the same fixed out-degree. We model a network generated by three mechanisms that are present in various networked systems; growth, global…