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Table 1 Summary of selected graph kernels: Computation by explicit (EX) and implicit (IM) feature mapping and support for attributed graphs

From: A survey on graph kernels

Graph kernelComputationLabelsAttributes
Shortest-Path (Borgwardt and Kriegel 2005)IM+ +
Generalized Shortest-Path (Hermansson et al. 2015)IM++
Graphlet (Shervashidze et al. 2009)EX
Cycles and Trees (Horváth et al. 2004)EX+
Tree Pattern Kernel (Ramon and Gärtner 2003; Mahé and Vert 2009)IM++
Ordered Directed Acyclic Graphs (Da San Martino et al. 2012a; 2012b)EX+
GraphHopper (Feragen et al. 2013)IM+ +
Graph Invariant (Orsini et al. 2015)IM++
Subgraph Matching (Kriege and Mutzel 2012)IM++
Weisfeiler-Lehman Subtree (Shervashidze et al. 2011)EX+
Weisfeiler-Lehman Edge (Shervashidze et al. 2011)EX+
Weisfeiler-Lehman Shortest-Path (Shervashidze et al. 2011)EX+
k-dim. Local Weisfeiler-Lehman Subtree (Morris et al. 2017)EX+
Neighborhood Hash Kernel (Hido and Kashima 2009)EX+
Propagation Kernel (Neumann et al. 2016)EX++
Neighborhood Subgraph Pairwise Distance Kernel (Costa and De Grave 2010)EX+
Random Walk (Gärtner et al. 2003; Kashima et al. 2003; Mahé et al. 2004; Vishwanathan et al. 2010; Sugiyama and Borgwardt 2015; Kang et al. 2012)IM++
Optimal Assignment Kernel (Fröhlich et al. 2005)IM++
Weisfeiler-Lehman Optimal Assignment (Kriege et al. 2016)IM+
Pyramid Match (Nikolentzos et al. 2017b)IM+
Matchings of Geometric Embeddings (Johansson and Dubhashi 2015)IM++
Descriptor Matching Kernel (Su et al. 2016)IM++
Graphlet Spectrum (Kondor et al. 2009)EX+
Multiscale Laplacian Graph Kernel (Kondor and Pan 2016)IM++
Global Graph Kernel (Johansson et al. 2014)EX
Deep Graph Kernels (Yanardag and Vishwanathan 2015a)IM+
Smoothed Graph Kernels (Yanardag and Vishwanathan 2015b)IM+
Hash Graph Kernel (Morris et al. 2016)EX++
Depth-based Representation Kernel (Bai et al. 2014)IM
Aligned Subtree Kernel (Bai et al. 2015)IM+
  1. The column ’Labels’ refers to whether the kernels support comparison of graphs with discrete vertex and edge labels in a way that depends on the interplay between structure and labels. The column ’Attributes’ refer to the same capability but for continuous or more general vertex attributes. — not considered in publication, but method can be extended; — vertex annotations only