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 ...

Thomassen characterized some 1-plane embedding as the forbidden configuration such that a given 1-plane embedding of a graph is drawable in straight-lines if and only if it does not contain the configuration [C. Thomassen, Rectilinear drawings of graphs, J. Graph Theory, 10(3), 335-341, 1988]. In this paper, we characterize some 1-plane embedding as the forbidden configuration such that a given...

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 applications such as node classification, node recommendation, link prediction, etc. However, most graph analytics methods suffer the high computation and space cost. ...

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...

Task mapping in modern high performance parallel computers can be modeled as a graph embedding problem, which simulates the mapping as embedding one graph into another and try to find the minimum wirelength for the mapping. Though embedding problems have been considered for several regular graphs, such as hypercubes into grids, binary trees into grids, et al, it is still an open problem for hyp...

We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given and another where the mapping is not given. In particular, we show that without mapping, any number of outerplanar graphs can be embedded simultaneously on an O(n)×O(n) grid, and an outerplanar and general planar gra...

In this paper, we propose the Directed Graph Embedding (DGE) method that embeds vertices on a directed graph into a vector space by considering the link structure of graphs. The basic idea is to preserve the locality property of vertices on a directed graph in the embedded space. We use the transition probability together with the stationary distribution of Markov random walks to measure such l...

Given a graph G with n vertices and a set S of n points in the plane, a point-set embedding of G on S is a planar drawing such that each vertex of G is mapped to a distinct point of S. A straight-line point-set embedding is a point-set embedding with no edge bends or curves. The point-set embeddability problem is NP-complete, even when G is 2-connected and 2-outerplanar. It has been solved poly...

Many real-world networks have a rich collection of objects. The semantics of these objects allows us to capture different classes of proximities, thus enabling an important task of semantic proximity search. As the core of semantic proximity search, we have to measure the proximity on a heterogeneous graph, whose nodes are various types of objects. Most of the existing methods rely on engineeri...

The depth of a planar embedding is a measure of the topological nesting of the biconnected components of the graph. Minimizing the depth of planar embeddings has important practical applications to graph drawing. We give a linear time algorithm for computing a minimum depth embedding of a planar graphs whose biconnected components have a prescribed embedding.