Graph embedding provides an ecient solution for graph analysis by converting the graph into a low-dimensional space which preserves the structure information. In contrast to the graph structure data, the i.i.d. node embeddings can be processed eciently in terms of both time and space. Current semi-supervised graph embedding algorithms assume the labelled nodes are given, which may not be alwa...

A new simple algorithm for optimal embedding of complete binary trees into hypercubes as well as a node-by-node algorithm for embedding of nearly complete binary trees into hypercubes are presented.

Network embedding in heterogeneous information networks (HINs) is a challenging task, due to complications of different node types and rich relationships between nodes. As a result, conventional network embedding techniques cannot work on such HINs. Recently, metapathbased approaches have been proposed to characterize relationships in HINs, but they are ineffective in capturing rich contexts an...

Abstract Graph is a generic model of various networks in real-world applications. And, graph embedding aims to represent nodes (edges or graphs) as low-dimensional vectors which can be fed into machine learning algorithms for downstream analysis tasks. However, existing random walk-based node methods often map some with (dis)similar local structures (near) far vectors. To overcome this issue, p...

Recent advances in language modeling such as word2vec motivate a number of graph embedding approaches by treating random walk sequences as sentences to encode structural proximity in a graph. However, most of the existing principles of neural graph embedding do not incorporate auxiliary information such as node content flexibly. In this paper we take a matrix factorization perspective of graph ...

Network embedding leverages the node proximity manifested to learn a low-dimensional node vector representation for each node in the network. Œe learned embeddings could advance various learning tasks such as node classi€cation, network clustering, and link prediction. Most, if not all, of the existing works, are overwhelmingly performed in the context of plain and static networks. Nonetheless,...

In this article, several schemes are proposed for embedding complete binary trees (CBT) into meshes. All of the proposed methods outperform those in the previous studies. First, a link congestion 1 embedding is achieved. Its expansion ratio is at the lowest level as we know now. Except for this superiority, it also provides another capability for fault tolerance to resist abnormal system faults...

This paper introduces a type of graph embedding called a mutual embedding. A mutual embedding between two n-node graphs G1 = (V1, E1) and G2 = (V2, E2) is an identification of the vertices of V1 and V2, i.e., a bijection π : V1 → V2, together with an embedding of G1 into G2 and an embedding of G2 into G1 where in the embedding of G1 into G2, each node u of G1 is mapped to π(u) in G2 and in the ...