Related papers: Generalized network structures: The configuration …

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…

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…

Random network models, constrained to reproduce specific statistical features, are often used to represent and analyze network data and their mathematical descriptions. Chief among them, the configuration model constrains random networks by…

A simplicial complex is a generalization of a graph: a collection of n-ary relationships (instead of binary as the edges of a graph), named simplices. In this paper, we develop a new tool to study the structure of simplicial complexes: we…

Motivated by the relevance of higher-order interactions in quantum physics and materials science at the nanoscale, recently a model has been introduced for new classes of networks that grow by the geometrically constrained aggregation of…

Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and…

There is increasing evidence that dense networks occur in on-line social networks, recommendation networks and in the brain. In addition to being dense, these networks are often also scale-free, i.e. their degree distributions follow…

We study complex networks formed by triangulations and higher-dimensional simplicial complexes representing closed evolving manifolds. In particular, for triangulations, the set of possible transformations of these networks is restricted by…

We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…

Motivation: Protein-protein interactions (PPIs) are usually modelled as networks. These networks have extensively been studied using graphlets, small induced subgraphs capturing the local wiring patterns around nodes in networks. They…

Graphs are ubiquitous to model the irregular (non-Euclidean) structure of complex data, but they are limited to pairwise relationships and fail to model the complexities of the datasets exhibiting higher-order interactions. In that context,…

In this paper we introduce and study a new family of combinatorial simplicial complexes, which we call immediate snapshot complexes. Our construction and terminology is strongly motivated by theoretical distributed computing, as these…

Over the last two decades, network science has greatly advanced our understanding of how the collective behaviors of a complex system emerge from the interactions among its basic units. Multiplex networks, i.e. networks with many layers,…

The presence of higher-order interactions (simplicial complexes) in networks and certain types of multilayer networks has shown to lead to the abrupt first-order transition to synchronization. We discover that simplicial complexes on…

Network representations of systems from various scientific and societal domains are neither completely random nor fully regular, but instead appear to contain recurring structural building blocks. These features tend to be shared by…

Complex networks are a powerful modeling tool, allowing the study of countless real-world systems. They have been used in very different domains such as computer science, biology, sociology, management, etc. Authors have been trying to…

Cascades arise in many contexts (e.g., neuronal avalanches, social contagions, and system failures). Despite evidence that propagations often involve higher-order dependencies, cascade theory has largely focused on models with…

In order to deal efficiently with the exponential growth of the Web services landscape in composition life cycle activities, it is necessary to have a clear view of its main features. As for many situations where there is a lot of…

Large software projects are among most sophisticated human-made systems consisting of a network of interdependent parts. Past studies of software systems from the perspective of complex networks have already led to notable discoveries with…

This paper introduces a data structure, called simplex tree, to represent abstract simplicial complexes of any dimension. All faces of the simplicial complex are explicitly stored in a trie whose nodes are in bijection with the faces of the…