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The study of complex networks has been historically based on simple graph data models representing relationships between individuals. However, often reality cannot be accurately captured by a flat graph model. This has led to the…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
Network theory provides tools which are particularly appropriate for assessing the complex interdependencies that characterise our modern connected world. This article presents an introduction to network theory, in a way that doesn't…
Degree correlation is an important topological property common to many real-world networks. In this paper, the statistical measures for characterizing the degree correlation in networks are investigated analytically. We give an exact proof…
Data-driven analysis of complex networks has been in the focus of research for decades. An important area of research is to study how well real networks can be described with a small selection of metrics, furthermore how well network models…
Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…
Many complex networks demonstrate a phenomenon of striking degree correlations, i.e., a node tends to link to other nodes with similar (or dissimilar) degrees. From the perspective of degree correlations, this paper attempts to characterize…
Modeling and topological analysis of networks in biological and other complex systems, must venture beyond the limited consideration of very few network metrics like degree, betweenness or assortativity. A proper identification of…
Homophily, the tendency of individuals to connect with others who share similar attributes, is a defining feature of social networks. Understanding how groups interact, both within and across, is crucial for uncovering the dynamics of…
Many real-world complex networks actually have a bipartite nature: their nodes may be separated into two classes, the links being between nodes of different classes only. Despite this, and despite the fact that many ad-hoc tools have been…
In the last years complex networks tools contributed to provide insights on the structure of research, through the study of collaboration, citation and co-occurrence networks. The network approach focuses on pairwise relationships, often…
In a recent work \cite{LiuJoladSchZia13}, we introduced dynamic networks with preferred degrees and presented simulation and analytic studies of a single, homogeneous system as well as two interacting networks. Here, we extend these studies…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
Introduced recently, the concept of hierarchical degree allows a more complete characterization of the topological context of a node in a complex network than the traditional node degree. This article presents analytical characterization…
Networks are convenient mathematical models to represent the structure of complex systems, from cells to societies. In the past decade, multilayer network science -- the branch of the field dealing with units interacting in multiple…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
Collective behavior plays a key role in the function of a wide range of physical, biological, and neurological systems where empirical evidence has recently uncovered the prevalence of higher-order interactions, i.e., structures that…
Looking to overcome the limitations of traditional networks, the network science community has lately given much attention to the so-called higher-order networks, where group interactions are modeled alongside pairwise ones. While degree…
What do societies, the Internet, and the human brain have in common? They are all examples of complex relational systems, whose emerging behaviours are largely determined by the non-trivial networks of interactions among their constituents,…
Large scale real-world network data such as social and information networks are ubiquitous. The study of such social and information networks seeks to find patterns and explain their emergence through tractable models. In most networks, and…