A Z-linkless embedding of a graph is an embedding in 3-space such that each pair of disjoint circuits has zero linking number. In this paper we present polynomial-time algorithms to compute a Z-linkless embedding of a graph provided the graph has one and to test whether an embedding of a graph is Z-linkless or not.

Many real-life networks can be modelled by stochastic processes with a spatial embedding. In such processes, the link probability decreases with distance. Using the theory of graph limits, we show how to recognize graph sequences produced by random graph processes with a linear embedding (a natural embedding into R). We define an operator Γ which applies to graph limits, which assumes the value...

Recently there has been a surge of interest in designing graph embedding methods. Few, if any, can scale to a large-sized graph with millions of nodes due to both computational complexity and memory requirements. In this paper, we relax this limitation by introducing the MultI-Level Embedding (MILE) framework – a generic methodology allowing contemporary graph embedding methods to scale to larg...

Knowledge graph embedding (KGE), which maps entities and relations in a knowledge into continuous vector spaces, has achieved great success predicting missing links graphs. However, graphs often contain incomplete triples that are difficult to inductively infer by KGEs. To address this challenge, we resort analogical inference propose novel general self-supervised framework AnKGE enhance KGE mo...

The quadratic embedding constant (QE constant) of a graph is new characteristic value defined through the distance matrix. We derive formulae for QE constants join two regular graphs, double graphs and certain lexicographic product graphs. Examples include complete bipartite wheel friendship completely split graph, some associated to strongly