相关论文: Clique Topology Reveals Intrinsic Geometric Struct…

High-dimensional neural activity often reside in a low-dimensional subspace, referred to as neural manifolds. Grid cells in the medial entorhinal cortex provide a periodic spatial code that are organized near a toroidal manifold,…

A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…

This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…

Structural features are important features in a geometrical graph. Although there are some correlation analysis of features based on covariance, there is no relevant research on structural feature correlation analysis with graph neural…

We introduce new algebro-topological invariants of directed networks, based on the topological construction of the directed clique complex. The shape of the underlying directed graph is encoded in a way that can be studied mathematically to…

Different classes of communication network topologies and their representation in the form of adjacency matrix and its eigenvalues are presented. A self-organizing feature map neural network is used to map different classes of communication…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

Motivated by an approach to visualization of high dimensional statistical data given in Hurley and Oldford (2011), this work examines the clique structure of $J_n(m, m-1)$ Johnson graphs. Cliques and maximal cliques are characterized and…

Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…

We present a numerical analysis of local community assembly through weak migration from a regional species pool. At equilibrium, the local community consists of a subset ("clique") of species from the regional community. Our analysis…

We propose the n-clique network as a powerful tool for understanding global structures of combined highly-interconnected subgraphs, and provide theoretical predictions for statistical properties of the n-clique networks embedded in a…

We study clustering properties of networks of single integrator nodes over a directed graph, in which the nodes converge to steady-state values. These values define clustering groups of nodes, which depend on interaction topology, edge…

Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures. These models aggregate signals over such…

A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…

Connection graphs (CGs) extend traditional graph models by coupling network topology with orthogonal transformations, enabling the representation of global geometric consistency. They play a key role in applications such as synchronization,…

In present paper we discuss several approaches to reconstructing the topology of the physical space from neural activity data of CA1 fields in mice hippocampus, in particular, having Cognitome theory of brain function in mind. In our…

One of the paramount challenges in neuroscience is to understand the dynamics of individual neurons and how they give rise to network dynamics when interconnected. Historically, researchers have resorted to graph theory, statistics, and…

The clique complex of a graph G is a simplicial complex whose simplices are all the cliques of G, and the line graph L(G) of G is a graph whose vertices are the edges of G and the edges of L(G) are incident edges of G. In this article, we…

Considering a clique as a conservative definition of community structure, we examine how graph partitioning algorithms interact with cliques. Many popular community-finding algorithms partition the entire graph into non-overlapping…

Complex networks contain complete subgraphs such as nodes, edges, triangles, etc., referred to as simplices and cliques of different orders. Notably, cavities consisting of higher-order cliques play an important role in brain functions.…