Related papers: Dynamical systems on graphs through the signless L…
Dynamical Systems (DS) are fundamental to the modeling and understanding time evolving phenomena, and have application in physics, biology and control. As determining an analytical description of the dynamics is often difficult, data-driven…
A broad range of applications involve signals with irregular structures that can be represented as a graph. As the underlying structures can change over time, the tracking dynamic graph topologies from observed signals is a fundamental…
This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…
One of the more challenging tasks in the understanding of dynamical properties of models on top of complex networks is to capture the precise role of multiplex topologies. In a recent paper, Gomez et al. [Phys. Rev. Lett. 101, 028701…
In the past two decades, the field of applied finance has tremendously benefited from graph theory. As a result, novel methods ranging from asset network estimation to hierarchical asset selection and portfolio allocation are now part of…
The properties of a hypergraph explored through the spectrum of its unified matrix was made by the authors in [26]. In this paper, we introduce three different hypergraph matrices: unified Laplacian matrix, unified signless Laplacian…
Many tools from the field of graph signal processing exploit knowledge of the underlying graph's structure (e.g., as encoded in the Laplacian matrix) to process signals on the graph. Therefore, in the case when no graph is available, graph…
Understanding the mutual interdependence between the behavior of dynamical processes on networks and the underlying topologies promises new insight for a large class of empirical networks. We present a generic approach to investigate this…
The eigenvalues of the Laplacian matrix for a class of directed graphs with both positive and negative weights are studied. First, a class of directed signed graphs is investigated in which one pair of nodes (either connected or not) is…
The signless Laplacian matrix of a graph $G$ is defined to be the sum of its adjacency matrix and degree diagonal matrix, and its eigenvalues are called $Q$-eigenvalues of $G$. A $Q$-eigenvalue of a graph $G$ is called a $Q$-main eigenvalue…
This study introduces a new metric called ''DynamicScore'' to evaluate the dynamics of graphs. It can be applied to both vertices and edges. Unlike traditional metrics, DynamicScore not only measures changes in the number of vertices or…
Although it is unambiguously agreed that structure plays a fundamental role in shaping the dynamics of complex systems, this intricate relationship still remains unclear. We investigate a general computational transformation by which we can…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
A finite discrete graph is turned into a quantum (metric) graph once a finite length is assigned to each edge and the one-dimensional Laplacian is taken to be the operator. We study the dependence of the spectral gap (the first positive…
A signless Laplacian eigenvalue of a graph $G$ is called a main signless Laplacian eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, all connected bicyclic graphs with exactly two main…
By studying varies dynamical processes, including coupled maps, cellular automata and coupled differential equations, on five different kinds of known networks, we found a positive relation between signal correlation and node's degree. Thus…
The study of time-varying (dynamic) networks (graphs) is of fundamental importance for computer network analytics. Several methods have been proposed to detect the effect of significant structural changes in a time series of graphs. The…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
We show several sharp upper and lower bounds for the sum of the largest eigenvalues of the signless Laplacian matrix. These bounds improve and extend previously known bounds.