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Many problems such as node classification and link prediction in network data can be solved using graph embeddings. However, it is difficult to use graphs to capture non-binary relations such as communities of nodes. These kinds of complex…
We prove that a Cayley graph can be embedded in the euclidean plane without accumulation points of vertices if and only if it is the 1-skeleton of a Cayley complex that can be embedded in the plane after removing redundant simplices. We…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
We investigate the problem of multiplex graph embedding, that is, graphs in which nodes interact through multiple types of relations (dimensions). In recent years, several methods have been developed to address this problem. However, the…
We present a novel graph diffusion-embedding networks (GDEN) for graph structured data. GDEN is motivated by our closed-form formulation on regularized feature diffusion on graph. GDEN integrates both regularized feature diffusion and…
This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding…
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…
High-performance computing (HPC) systems increasingly support both scalable AI training and large-scale simulation workloads. Both typically rely heavily on collective communication operations. On modern supercomputers, however, network…
We propose a representation of graph as a functional object derived from the power iteration of the underlying adjacency matrix. The proposed functional representation is a graph invariant, i.e., the functional remains unchanged under any…
This paper introduces a new class of efficient inter connection networks called as M-graphs for large multi-processor systems.The concept of M-matrix and M-graph is an extension of Mn-matrices and Mn-graphs.We analyze these M-graphs…
Convolutional neural network (CNN) architectures utilize downsampling layers, which restrict the subsequent layers to learn spatially invariant features while reducing computational costs. However, such a downsampling operation makes it…
Graph is a well known data structure to represent the associated relationships in a variety of applications, e.g., data science and machine learning. Despite a wealth of existing efforts on developing graph processing systems for improving…
Higher-order connectivity patterns such as small induced sub-graphs called graphlets (network motifs) are vital to understand the important components (modules/functional units) governing the configuration and behavior of complex networks.…
Theoretical results from discrete geometry suggest that normed spaces can abstractly embed finite metric spaces with surprisingly low theoretical bounds on distortion in low dimensions. In this paper, inspired by this theoretical insight,…
The generalized $k$-connectivity of a graph $G$, denoted by $\kappa_k(G)$, is the minimum number of internally edge disjoint $S$-trees for any $S\subseteq V(G)$ and $|S|=k$. The generalized $k$-connectivity is a natural extension of the…
Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect…
Daisy cubes are a recently introduced class of isometric subgraphs of hypercubes $Q_n$. They are induced with intervals between chosen vertices of $Q_n$ and the vertex $0^n\in V(Q_n)$. In this paper we characterize daisy cubes in terms of…
High-dimensional multiplex graphs are characterized by their high number of complementary and divergent dimensions. The existence of multiple hierarchical latent relations between the graph dimensions poses significant challenges to…
Heterogeneous graphs (HGs) also known as heterogeneous information networks have become ubiquitous in real-world scenarios; therefore, HG embedding, which aims to learn representations in a lower-dimension space while preserving the…
A network embedding is a representation of a large graph in a low-dimensional space, where vertices are modeled as vectors. The objective of a good embedding is to preserve the proximity between vertices in the original graph. This way,…