Related papers: Consensus and Coherence in Fractal Networks
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
Network filtering is an important form of dimension reduction to isolate the core constituents of large and interconnected complex systems. We introduce a new technique to filter large dimensional networks arising out of dynamical behavior…
High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…
In this paper, we consider the random walk process on a kind of fractal (or transfractal) scale free networks, which also called as $(u,v)$ flowers, and we focus on the global first passage time (GFPT) and first return time (FRT). Here, we…
We report an approach to obtaining complex networks with diverse topology, here called syntonets, taking into account the consonances and dissonances between notes as defined by scale temperaments. Though the fundamental frequency is…
A heterogeneous continuous time random walk is an analytical formalism for studying and modeling diffusion processes in heterogeneous structures on microscopic and macroscopic scales. In this paper we study both analytically and numerically…
The problem of model selection arises in a number of contexts, such as compressed sensing, subset selection in linear regression, estimation of structures in graphical models, and signal denoising. This paper generalizes the notion of…
Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little…
Community identification of network components enables us to understand the mesoscale clustering structure of networks. A number of algorithms have been developed to determine the most likely community structures in networks. Such a…
We discuss a one-dimensional model of a fluctuating interface with a dynamic exponent $z=1$. The events that occur are adsorption, which is local, and desorption which is non-local and may take place over regions of the order of the system…
How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…
We study the asymptotic properties of distributed consensus algorithms over switching directed random networks. More specifically, we focus on consensus algorithms over independent and identically distributed, directed random graphs, where…
We study fully synchronized (coherent) states in complex networks of chaotic oscillators, reviewing the analytical approach of determining the stability conditions for synchronizability and comparing them with numerical criteria. As an…
Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
Community detection is of fundamental significance for understanding the topology characters and the spreading dynamics on complex networks. While random walk is widely used and is proven effective in many community detection algorithms,…
In this paper, we consider the $\mathcal{H}_2$-norm of networked systems with multi-time scale consensus dynamics and vector-valued agent states. This allows us to explore how measurement and process noise affect consensus on…
We investigate how the graph topology influences the robustness to noise in undirected linear consensus networks. We measure the structural robustness by using the smallest possible value of steady state population variance of states under…
Traffic networks have been proved to be fractal systems. However, previous studies mainly focused on monofractal networks, while complex systems are of multifractal structure. This paper is devoted to exploring the general regularities of…
We consider \emph{plurality consensus} in a network of $n$ nodes. Initially, each node has one of $k$ opinions. The nodes execute a (randomized) distributed protocol to agree on the plurality opinion (the opinion initially supported by the…