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We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
Graph are a ubiquitous data representation, as they represent a flexible and compact representation. For instance, the 3D structure of RNA can be efficiently represented as $\textit{2.5D graphs}$, graphs whose nodes are nucleotides and…
Graphs and various graph-like combinatorial structures, such as preorders and hypergraphs, are ubiquitous in programming. This paper focuses on representing graphs in a purely functional programming language like Haskell. There are several…
Lots of neural network architectures have been proposed to deal with learning tasks on graph-structured data. However, most of these models concentrate on only node features during the learning process. The edge features, which usually play…
Graphs are a representation of structured data that captures the relationships between sets of objects. With the ubiquity of available network data, there is increasing industrial and academic need to quickly analyze graphs with billions of…
Many, if not most network analysis algorithms have been designed specifically for single-relational networks; that is, networks in which all edges are of the same type. For example, edges may either represent "friendship," "kinship," or…
Program source code contains complex structure information, which can be represented in structured data forms like trees or graphs. To acquire the structural information in source code, most existing researches use abstract syntax trees…
Graph representation learning aim at integrating node contents with graph structure to learn nodes/graph representations. Nevertheless, it is found that many existing graph learning methods do not work well on data with high heterophily…
Consider an algebraic identity between elliptic modular graphs where several vertices are at fixed locations (and hence unintegrated) while the others are integrated over the toroidal worldsheet. At any unintegrated vertex, we can glue an…
Representation learning provides new and powerful graph analytical approaches and tools for the highly valued data science challenge of mining knowledge graphs. Since previous graph analytical methods have mostly focused on homogeneous…
In the real world, networks often contain multiple relationships among nodes, manifested as the heterogeneity of the edges in the networks. We convert the heterogeneous networks into multiple views by using each view to describe a specific…
The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…
In this article, we extend several algebraic graph analysis methods to bipartite networks. In various areas of science, engineering and commerce, many types of information can be represented as networks, and thus the discipline of network…
The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. Mathematically the Graph- BLAS defines a core set of matrix-based graph operations that can…
Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…
A graph is a data structure composed of dots (i.e. vertices) and lines (i.e. edges). The dots and lines of a graph can be organized into intricate arrangements. The ability for a graph to denote objects and their relationships to one…
Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…
Important graph mining problems such as Clustering are computationally demanding. To significantly accelerate these problems, we propose ProbGraph: a graph representation that enables simple and fast approximate parallel graph mining with…
Graph representation learning (GRL) is to encode graph elements into informative vector representations, which can be used in downstream tasks for analyzing graph-structured data and has seen extensive applications in various domains.…
Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets. Out of this mathematical impossibility emerges the question…