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Identifying the importance of nodes of complex networks is of interest to the research of Social Networks, Biological Networks etc.. Current researchers have proposed several measures or algorithms, such as betweenness, PageRank and HITS…

In this paper, the ordered set of rough sets determined by a quasiorder relation $R$ is investigated. We prove that this ordered set is a complete, completely distributive lattice. We show that on this lattice can be defined three different…

A concept of higher order neighborhood in complex networks, introduced previously (PRE \textbf{73}, 046101, (2006)), is systematically explored to investigate larger scale structures in complex networks. The basic idea is to consider each…

Networks are complex models for underlying data in many application domains. In most instances, raw data is not natively in the form of a network, but derived from sensors, logs, images, or other data. Yet, the impact of the various choices…

The success of Deep Learning methods is not well understood, though various attempts at explaining it have been made, typically centered on properties of stochastic gradient descent. Even less clear is why certain neural network…

The current understanding of deep neural networks can only partially explain how input structure, network parameters and optimization algorithms jointly contribute to achieve the strong generalization power that is typically observed in…

As complex networks find applications in a growing range of disciplines, the diversity of naturally occurring and model networks being studied is exploding. The adoption of a well-developed collection of network taxonomies is a natural…

The relationship between network topology and system dynamics has significant implications for unifying our understanding of the interplay among metabolic, gene-regulatory, and ecosystem network architecures. Here we analyze the stability…

Higher-order network analysis uses the ideas of hypergraphs, simplicial complexes, multilinear and tensor algebra, and more, to study complex systems. These are by now well established mathematical abstractions. What's new is that the ideas…

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…

Chaos is an intriguing phenomenon that can be found in an immense variate of systems. Its detection and discrimination from its counterpart order poses an interesting challenge. To address it, we present a deep classifier capable of…

It is known for decades that computer-based systems cannot be understood without a concept of modularization and decomposition. We suggest a universal, expressive, intuitively attractive composition operator for Petri nets, combined with a…

Recent studies uncovered important core/periphery network structures characterizing complex sets of cooperative and competitive interactions between network nodes, be they proteins, cells, species or humans. Better characterization of the…

We compare the structural properties of the street networks of ten different European cities using their primal representation. We investigate the properties of the geometry of the networks and a set of centrality measures highlighting…

In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant…

A principled approach to understand network structures is to formulate generative models. Given a collection of models, however, an outstanding key task is to determine which one provides a more accurate description of the network at hand,…

We introduce an informative labeling algorithm for the vertices of a family of Koch networks. Each of the labels is consisted of two parts, the precise position and the time adding to Koch networks. The shortest path routing between any two…

Driven by growing interest in the sciences, industry, and among the broader public, a large number of empirical studies have been conducted in recent years of the structure of networks ranging from the internet and the world wide web to…

Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…

Many neural nets appear to represent data as linear combinations of "feature vectors." Algorithms for discovering these vectors have seen impressive recent success. However, we argue that this success is incomplete without an understanding…