Quadratic embedding constants of path graphs

Quadratic Surface Embedding

We discuss various primal and dual algorithms for multidimensional scaling with spherical, ellipsoidal, and more general quadratic constraints. Distances between points on the surface can be either measured along Euclidean lines or along shortest geodesics on the surface.

α Valuations of Special Classes of Quadratic Graphs

Joint Embedding of Graphs

Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a method to jointly embed multiple undirected graphs. Given a set of graphs, the joint embedding method identifies a linear subspace spanned by rank one symmetr...

Embedding Graphs into Embedded Graphs

A drawing of a graph G in the plane is weakly simple if it can be turned into an embedding by an arbitrarily small perturbation. We show that testing, whether a straight-line drawing of a planar graph G in the plane is weakly simple, can be carried out in polynomial time, if a desired embedding of G belongs to a fixed isotopy class. In other words, we show that c-planarity with pipes is tractab...

Spectral embedding of graphs

In this paper we explore how to embed symbolic relational graphs with unweighted edges in a pattern-space. We adopt a graph-spectral approach. We use the leading eigenvectors of the graph adjacency matrix to de0ne eigenmodes of the adjacency matrix. For each eigenmode, we compute vectors of spectral properties. These include the eigenmode perimeter, eigenmode volume, Cheeger number, inter-mode ...