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Using particle-scale models to accurately describe property enhancements and phase transitions in macroscopic behavior is a major engineering challenge in composite materials science. To address some of these challenges, we use the graph…
We will consider P-graph complexes, where P is a cyclic operad. P-graph complexes are natural generalizations of Kontsevich's graph complexes -- for P = the operad for associative algebras it is the complex of ribbon graphs, for P = the…
Graph convolutional neural networks (GCN) have been the model of choice for graph representation learning, which is mainly due to the effective design of graph convolution that computes the representation of a node by aggregating those of…
Learning representation on graph plays a crucial role in numerous tasks of pattern recognition. Different from grid-shaped images/videos, on which local convolution kernels can be lattices, however, graphs are fully coordinate-free on…
Let $H_n$ be a graph on $n$ vertices and let $\ber{H_n}$ denote the complement of $H_n$. Suppose that $\Delta = \Delta(n)$ is the maximum degree of $\ber{H_n}$. We analyse three algorithms for sampling $d$-regular subgraphs ($d$-factors) of…
Graph data often exhibits complex geometric heterogeneity, where structures with varying local curvature, such as tree-like hierarchies and dense communities, coexist within a single network. Existing geometric GNNs, which embed graphs into…
A $\mathbb{T}$-gain graph is a simple graph in which a unit complex number is assigned to each orientation of an edge, and its inverse is assigned to the opposite orientation. The associated adjacency matrix is defined canonically, and is…
Oriented ribbon graphs (dessins d'enfant) are graphs embedded in oriented surfaces. A quasi-tree of a ribbon graph is a spanning subgraph with one face, which is described by an ordered chord diagram. We show that for any link diagram $L$,…
Graph representation learning (a.k.a. network embedding) is a significant topic of network analysis, due to its effectiveness to support various graph inference tasks. In this paper, we study the representation learning with multiple…
Graph Convolutional Networks (GCNs) have been widely used due to their outstanding performance in processing graph-structured data. However, the undirected graphs limit their application scope. In this paper, we extend spectral-based graph…
If Gamma is any finite graph, then the unlabelled configuration space of n points on Gamma, denoted UC^n(Gamma), is the space of n-element subsets of Gamma. The braid group of Gamma on n strands is the fundamental group of UC^n(Gamma). We…
Convolutional neural networks (CNNs) have achieved great success on grid-like data such as images, but face tremendous challenges in learning from more generic data such as graphs. In CNNs, the trainable local filters enable the automatic…
The neighborhood complex of a graph was introduced by Lov\'asz to provide topological lower bounds on chromatic number. More general homomorphism complexes of graphs were further studied by Babson and Kozlov. Such `Hom complexes' are also…
Graph Neural Networks (GNNs) draw their strength from explicitly modeling the topological information of structured data. However, existing GNNs suffer from limited capability in capturing the hierarchical graph representation which plays…
Recent advancements in Graph Neural Networks have led to state-of-the-art performance on graph representation learning. However, the majority of existing works process directed graphs by symmetrization, which causes loss of directional…
Federated Graph Learning (FGL) has demonstrated the advantage of training a global Graph Neural Network (GNN) model across distributed clients using their local graph data. Unlike Euclidean data (\eg, images), graph data is composed of…
We focus on graph-to-sequence learning, which can be framed as transducing graph structures to sequences for text generation. To capture structural information associated with graphs, we investigate the problem of encoding graphs using…
The increasing prevalence of large-scale hypergraphs poses significant computational challenges for hypergraph neural network (HNN) training. To address this, hypergraph condensation (HGC) distills large real hypergraphs into compact yet…
Recent works have made great progress in semantic segmentation by exploiting contextual information in a local or global manner with dilated convolutions, pyramid pooling or self-attention mechanism. In order to avoid potential misleading…
This paper extends results of Hatcher and Vogtmann's work "Cerf Theory for Graphs" to ribbon graphs. Given an orientable, punctured and basepointed surface Sigma, we prove that the space of ribbon graphs that can be drawn in Sigma is…