Related papers: How Complex is a Complex Network? Insights from Li…
While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be…
The rapid evolution of network services demands new paradigms for studying and designing networks. In order to understand the underlying mechanisms that provide network functions, we propose a framework which enables the functional analysis…
We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all…
Real-world complex systems exhibit multiple levels of relationships. In many cases, they require to be modeled by interconnected multilayer networks, characterizing interactions on several levels simultaneously. It is of crucial importance…
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…
We define a notion of complexity, which quantifies the nonlinearity of the computation of a neural network, as well as a complementary measure of the effective dimension of feature representations. We investigate these observables both for…
The structure entropy is an important index to illuminate the structure property of the complex network. Most of the existing structure entropies are based on the degree distribution of the complex network. But the structure entropy based…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: It requires an accurate map of the network that governs the interactions between the…
Complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from…
The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
Finding the important nodes in complex networks by topological structure is of great significance to network invulnerability. Several centrality measures have been proposed recently to evaluate the performance of nodes based on their…
Complex networks in natural, social, and technological systems generically exhibit an abundance of rich information. Extracting meaningful structural features from data is one of the most challenging tasks in network theory. Many methods…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
Many complex systems can be represented as networks and separating a network into communities could simplify the functional analysis considerably. Recently, many approaches have been proposed for finding communities, but none of them can…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally…
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…
A good deal of current research in complex networks involves the characterization and/or classification of the topological properties of given structures, which has motivated several respective measurements. This letter proposes a framework…