Related papers: A spectral graph theoretic study of predator-prey …
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
In light of the rise of malicious attacks on the Internet, and the various networks and applications attached to it, new approaches towards modeling predatory activity in networks could be useful. Past research has simulated networks…
Many methods have been developed for finding the commonalities between different organisms to study their phylogeny. The structure of metabolic networks also reveal valuable insights into metabolic capacity of species as well as into the…
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 destinations, has been argued to…
The behavior of ecological systems mainly relies on the interactions between the species it involves. We consider the problem of inferring the species interaction network from abundance data. To be relevant, any network inference…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
Network topology inference is a cornerstone problem in statistical analyses of complex systems. In this context, the fresh look advocated here permeates benefits from convex optimization and graph signal processing, to identify the…
To the best of our knowledge, this paper presents the first large-scale study that tests whether network categories (e.g., social networks vs. web graphs) are distinguishable from one another (using both categories of real-world networks…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics…
Biomolecular networks have already found great utility in characterizing complex biological systems arising from pair-wise interactions amongst biomolecules. Here, we review how graph theoretical approaches can be applied not only for a…
Graph signal processing (GSP) is a key tool for satisfying the growing demand for information processing over networks. However, the success of GSP in downstream learning and inference tasks is heavily dependent on the prior identification…
Reaction-diffusion systems may lead to the formation of steady state heterogeneous spatial patterns, known as Turing patterns. Their mathematical formulation is important for the study of pattern formation in general and play central roles…
We propose two spectral algorithms for partitioning nodes in directed graphs respectively with a cyclic and an acyclic pattern of connection between groups of nodes. Our methods are based on the computation of extremal eigenvalues of the…
Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
The study of spectral graph determination is a fascinating area of research in spectral graph theory and algebraic combinatorics. This field focuses on examining the spectral characterization of various classes of graphs, developing methods…
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…