Flow fields are often partitioned into data blocks for massively parallel
computation and analysis based on blockwise relationships. However, most of the
previous techniques only consider the first-order dependencies among blocks,
which is insufficient in describing complex flow patterns. In this work, we
present FlowHON, an approach to construct higher-order networks (HONs) from
flow fields. FlowHON captures the inherent higher-order dependencies in flow
fields as nodes and estimates the transitions among them as edges. We formulate
the HON construction as an optimization problem with three linear
transformations. The first two layers correspond to the node generation and the
third one corresponds to edge estimation. Our formulation allows the node
generation and edge estimation to be solved in a unified framework. With
FlowHON, the rich set of traditional graph algorithms can be applied without
any modification to analyze flow fields, while leveraging the higher-order
information to understand the inherent structure and manage flow data for
efficiency. We demonstrate the effectiveness of FlowHON using a series of
downstream tasks, including estimating the density of particles during tracing,
partitioning flow fields for data management, and understanding flow fields
using the node-link diagram representation of networks.

使用 FlowHON 方法构建高阶网络来分析流场，并通过节点生成和边估计解决对流场的密度估计、数据管理和结构理解等下游任务。

FlowHON: 使用高阶网络表示流场

FlowHON: Representing Flow Fields Using Higher-Order Networks

Most of the current hypergraph learning methodologies and benchmarking
datasets in the hypergraph realm are obtained by lifting procedures from their
graph analogs, simultaneously leading to overshadowing hypergraph network
foundations. This paper attempts to confront some pending questions in that
regard: Can the concept of homophily play a crucial role in Hypergraph Neural
Networks (HGNNs), similar to its significance in graph-based research? Is there
room for improving current hypergraph architectures and methodologies? (e.g. by
carefully addressing the specific characteristics of higher-order networks) Do
existing datasets provide a meaningful benchmark for HGNNs? Diving into the
details, this paper proposes a novel conceptualization of homophily in
higher-order networks based on a message passing scheme; this approach
harmonizes the analytical frameworks of datasets and architectures, offering a
unified perspective for exploring and interpreting complex, higher-order
network structures and dynamics. Further, we propose MultiSet, a novel message
passing framework that redefines HGNNs by allowing hyperedge-dependent node
representations, as well as introduce a novel architecture MultiSetMixer that
leverages a new hyperedge sampling strategy. Finally, we provide an extensive
set of experiments that contextualize our proposals and lead to valuable
insights in hypergraph representation learning.

本论文旨在探讨超图学习方法和基准数据集的一些悬而未决的问题，其中提出了一种新的同质性概念，探索了高阶网络结构和动态的分析框架，并引入了 MultiSet 框架重新定义 Hypergraph Neural Networks。

基于消息传递的超图神经网络：同质性和架构设计的共同视角

Hypergraph Neural Networks through the Lens of Message Passing: A Common  Perspective to Homophily and Architecture Design

Core-periphery detection is a key task in exploratory network analysis where
one aims to find a core, a set of nodes well-connected internally and with the
periphery, and a periphery, a set of nodes connected only (or mostly) with the
core. In this work we propose a model of core-periphery for higher-order
networks modeled as hypergraphs and we propose a method for computing a
core-score vector that quantifies how close each node is to the core. In
particular, we show that this method solves the corresponding non-convex
core-periphery optimization problem globally to an arbitrary precision. This
method turns out to coincide with the computation of the Perron eigenvector of
a nonlinear hypergraph operator, suitably defined in term of the incidence
matrix of the hypergraph, generalizing recently proposed centrality models for
hypergraphs. We perform several experiments on synthetic and real-world
hypergraphs showing that the proposed method outperforms alternative
core-periphery detection algorithms, in particular those obtained by
transferring established graph methods to the hypergraph setting via clique
expansion.

本文提出了一种基于超图的核心 - 边缘模型，通过对高阶网络的核心分数向量进行计算，解决了对应的非凸核心 - 边缘优化问题，被证明在人工合成和真实世界的网络数据集中表现得比竞争算法要好。