Related papers: Random Matrix Analysis of Multiplex Networks
Network structure provides critical information for understanding the dynamic behavior of networks. However, the complete structure of real-world networks is often unavailable, thus it is crucially important to develop approaches to infer a…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…
Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered…
We introduce a new family of $N\times N$ random real symmetric matrix ensembles, the $k$-checkerboard matrices, whose limiting spectral measure has two components which can be determined explicitly. All but $k$ eigenvalues are in the bulk,…
Network topologies can be non-trivial, due to the complex underlying behaviors that form them. While past research has shown that some processes on networks may be characterized by low-order statistics describing nodes and their neighbors,…
We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
Empirical networks are often globally sparse, with a small average number of connections per node, when compared to the total size of the network. However, this sparsity tends not to be homogeneous, and networks can also be locally dense,…
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…
The ratio of two consecutive level spacings has emerged as a very useful metric in investigating universal features exhibited by complex spectra. It does not require the knowledge of density of states and is therefore quite convenient to…
We present analytical results for the emerging structure of networks that evolve via a combination of growth (by node addition and random attachment) and contraction (by random node deletion). To this end we consider a network model in…
This is a cursory overview of applications of concepts from random matrix theory (RMT) to quantum electronics and classical & quantum optics. The emphasis is on phenomena, predicted or explained by RMT, that have actually been observed in…
A Random Geometric Graph (RGG) ensemble is defined by the disordered distribution of its node locations. We investigate how this randomness drives sample-to-sample fluctuations in the dynamical properties of these graphs. We study the…
Eigenvalues statistics of various many-body systems have been widely studied using the nearest neighbor spacing distribution under the random matrix theory framework. Here, we numerically analyze eigenvalue ratio statistics of multiplex…
Larger networks generally have greater representational power at the cost of increased computational complexity. Sparsifying such networks has been an active area of research but has been generally limited to static regularization or…
Three recently suggested random matrix ensembles (RME) are linked together by an exact mapping and plausible conjections. Since it is known that in one of these ensembles the eigenvector statistics is multifractal, we argue that all three…
In this work we investigate time varying networks with complex dynamics at the nodes. We consider two scenarios of network change in an interval of time: first, we have the case where each link can change with probability pt, i.e. the…
We have introduced a novel multiplex recurrence network (MRN) approach by combining recurrence networks with the multiplex network approach in order to investigate multivariate time series. The potential use of this approach is demonstrated…
Networks of strongly-coupled neurons with random connectivity exhibit chaotic, asynchronous fluctuations. In previous work, we showed that when endowed with an additional low-rank connectivity consisting of the outer product of orthogonal…
Brain connectivity networks, derived from magnetic resonance imaging (MRI), non-invasively quantify the relationship in function, structure, and morphology between two brain regions of interest (ROIs) and give insights into gender-related…