Over the last few years, graph autoencoders (AE) and variational (VAE) emerged as powerful node embedding methods, with promising performances on challenging tasks such link prediction clustering. Graph AE, VAE most of their extensions rely multi-layer convolutional networks (GCN) encoders to learn vector space representations nodes. In this paper, we show that GCN are actually unnecessarily co...

The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. An and Wu introduce the notion of list linear arboricity lla(G) of a graph G and conjecture that lla(G) = la(G) for any graph G. We confirm that this conjecture is true for any planar graph having ∆ > 13, or for any planar graph with ∆ > 7 and without i-cycles for some i ∈ {3, 4, 5}....

Graph kernels are powerful tools to bridge the gap between machine learning and data encoded as graphs. Most graph based on decomposition of graphs into a set patterns. The similarity two is then deduced corresponding Kernels linear patterns constitute good trade-off accuracy computational complexity. In this work, we propose thorough investigation comparison different patterns, namely walks pa...

We introduce a new notion of graph sparsificaiton based on spectral similarity of graph Laplacians: spectral sparsification requires that the Laplacian quadratic form of the sparsifier approximate that of the original. This is equivalent to saying that the Laplacian of the sparsifier is a good preconditioner for the Laplacian of the original. We prove that every graph has a spectral sparsifier ...