Related papers: Simplicial complexes in network intrusion profilin…

Many real networks in social sciences, biological and biomedical sciences or computer science have an inherent structure of simplicial complexes reflecting many-body interactions. Therefore, to analyse topological and dynamical properties…

Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…

Complex networks can be used to represent complex systems which originate in the real world. Here we study a transformation of these complex networks into simplicial complexes, where cliques represent the simplices of the complex. We extend…

Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes. Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social…

We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…

Cyberattacks on enterprise networks exploit complex dependencies among infrastructure, services, and applications, which challenge traditional analysis methods that focus on attack paths or network topology in isolation. In this study, we…

We outline a novel clustering scheme for simplicial complexes that produces clusters of simplices in a way that is sensitive to the homology of the complex. The method is inspired by, and can be seen as a higher-dimensional version of,…

Detecting anomalies in link streams that represent various kinds of interactions is an important research topic with crucial applications. Because of the lack of ground truth data, proposed methods are mostly evaluated through their ability…

Analyzing embedded simplicial complexes, such as triangular meshes and graphs, is an important problem in many fields. We propose a new approach for analyzing embedded simplicial complexes in a subdivision-invariant and isometry-invariant…

We analyze the time series obtained from different dynamical regimes of the logistic map by constructing their equivalent time series (TS) networks, using the visibility algorithm. The regimes analyzed include both periodic and chaotic…

This paper introduces a model that identifies spatial relationships for a structural analysis based on the concept of simplicial complex. The spatial relationships are identified through overlapping two map layers, namely a primary layer…

Simplicial complexes are higher-order combinatorial structures which have been used to represent real-world complex systems. In this paper, we concentrate on the local patterns in simplicial complexes called simplets, a generalization of…

The increasing interest in complex networks research has been a consequence of several intrinsic features of this area, such as the generality of the approach to represent and model virtually any discrete system, and the incorporation of…

We study the response of complex networks subject to attacks on vertices and edges. Several existing complex network models as well as real-world networks of scientific collaborations and Internet traffic are numerically investigated, and…

Graph-based classification methods are widely used for security and privacy analytics. Roughly speaking, graph-based classification methods include collective classification and graph neural network. Evading a graph-based classification…

Graphs can model networked data by representing them as nodes and their pairwise relationships as edges. Recently, signal processing and neural networks have been extended to process and learn from data on graphs, with achievements in tasks…

Many mobile networks are represented as graphs to obtain insight to their connectivity and transmission properties. Among these properties centrality resilience, that is, how well centralities, such as closeness and betweennesss, are…

Modern networked systems are constantly under threat from systemic attacks. There has been a massive upsurge in the number of devices connected to a network as well as the associated traffic volume. This has intensified the need to better…

Network Science provides a universal formalism for modelling and studying complex systems based on pairwise interactions between agents. However, many real networks in the social, biological or computer sciences involve interactions among…

We present simplicial neural networks (SNNs), a generalization of graph neural networks to data that live on a class of topological spaces called simplicial complexes. These are natural multi-dimensional extensions of graphs that encode not…