Related papers: Generalized network structures: The configuration …
Multiplex networks are complex graph structures in which a set of entities are connected to each other via multiple types of relations, each relation representing a distinct layer. Such graphs are used to investigate many complex…
We construct a natural generalized complex structure on the total space of any bundle endowed with a Chern connection and whose typical fibre is a homogeneous symplectic manifold. This extends known constructions of generalized complex…
Many graph products have been applied to generate complex networks with striking properties observed in real-world systems. In this paper, we propose a simple generative model for simplicial networks by iteratively using edge corona…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…
Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph…
We propose a generalized stochastic block model to explore the mesoscopic structures in signed networks by grouping vertices that exhibit similar positive and negative connection profiles into the same cluster. In this model, the group…
Many practical applications in topological data analysis arise from data in the form of point clouds, which then yield simplicial complexes. The combinatorial structure of simplicial complexes captures the topological relationships between…
Multiplex networks describe a large number of complex social, biological and transportation networks where a set of nodes is connected by links of different nature and connotation. Here we uncover the rich community structure of multiplex…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
Topological Signal Processing (TSP) over simplicial complexes is a framework that has been recently proposed, as a generalization of graph signal processing (GSP), to extend GSP to analyzing signals defined over sets of any order (i.e., not…
We propose a simplicial complex convolutional neural network (SCCNN) to learn data representations on simplicial complexes. It performs convolutions based on the multi-hop simplicial adjacencies via common faces and cofaces independently…
When describing complex interconnected systems, one often has to go beyond the standard network description to account for generalized interactions. Here, we establish a unified framework to simplify the stability analysis of cluster…
A number of machine learning models have been proposed with the goal of achieving systematic generalization: the ability to reason about new situations by combining aspects of previous experiences. These models leverage compositional…
Due to notable discoveries in the fast evolving field of complex networks, recent research in software engineering has also focused on representing software systems with networks. Previous work has observed that these networks follow…
Graph representation learning methods have mostly been limited to the modelling of node-wise interactions. Recently, there has been an increased interest in understanding how higher-order structures can be utilised to further enhance the…
In many studies, it is common to use binary (i.e., unweighted) edges to examine networks of entities that are either adjacent or not adjacent. Researchers have generalized such binary networks to incorporate edge weights, which allow one to…
In the framework of coupled cell systems, a coupled cell network describes graphically the dynamical dependencies between individual dynamical systems, the cells. The fundamental network of a network reveals the hidden symmetries of that…
Recently there has been an increasing interest in studying dynamical processes on networks exhibiting higher-order structures, such as simplicial complexes, where the dynamics acts above and beyond dyadic interactions. Using simulations or…
Analytical approaches to model the structure of complex networks can be distinguished into two groups according to whether they consider an intensive (e.g., fixed degree sequence and random otherwise) or an extensive (e.g., adjacency…
Large-scale network systems describe a wide class of complex dynamical systems composed of many interacting subsystems. A large number of subsystems and their high-dimensional dynamics often result in highly complex topology and dynamics,…