A Degeneracy Framework for Graph Similarity

Abstract

The problem of accurately measuring the similarity between graphs is at the core of many applications in a variety of disciplines. Most existing methods for graph similarity focus either on local or on global properties of graphs. However, even if graphs seem very similar from a local or a global perspective, they may exhibit different structure at different scales. In this paper, we present a general framework for graph similarity which takes into account structure at multiple different scales. The proposed framework capitalizes on the well-known k-core decomposition of graphs in order to build a hierarchy of nested subgraphs. We apply the framework to derive variants of four graph kernels, namely graphlet kernel, shortest-path kernel, Weisfeiler-Lehman subtree kernel, and pyramid match graph kernel. The framework is not limited to graph kernels, but can be applied to any graph comparison algorithm. The proposed framework is evaluated on several benchmark datasets for graph classification. In most cases, the core-based kernels achieve significant improvements in terms of classification accuracy over the base kernels, while their time complexity remains very attractive.

Learning Backtrackless Aligned-Spatial Graph Convolutional Networks for Graph Classification

“…Experimental Setup: We compare the performance of the proposed BASGCN model on graph classification applications with a) six alternative state-of-the-art graph kernels and b) twelve alternative state-of-the-art deep learning methods for graphs. Specifically, the graph kernels include 1) the Jensen-Tsallis q-difference kernel (JTQK) with q = 2 [37], 2) the Weisfeiler-Lehman subtree kernel (WLSK) [11], 3) the shortest path graph kernel (SPGK) [38], 4) the shortest path kernel based on core variants (CORE SP) [39], 5) the random walk graph kernel (RWGK) [40], and 6) the graphlet count kernel (GK) [41]. On the other hand, the deep learning methods include 1) the deep graph convolutional neural network (DGCNN) [31], 2) the PATCHY-SAN based convolutional neural network for graphs (PSGCNN) [32], 3) the diffusion convolutional neural network (DCNN) [25], 4) the deep graphlet kernel (DGK) [42], 5) the graph capsule convolutional neural network (GCCNN) [43], 6) the anonymous walk embeddings based on feature driven (AWE) [44], 7) the edge-conditioned convolutional networks (ECC) [45], 8) the high-order graph convolution network (HO-GCN) [46], 9) the graph convolution network based on Differentiable Pooling (DiffPool) [47], 10) the graph convolution network based on Self-Attention Pooling (SAGPool) [48], 11) the graph convolutional network with EigenPooling (EigenPool) [48], and 12) the degree-specific graph neural networks (DEMO-Net) [49].…”

Temporal Graph Kernels for Classifying Dissemination Processes

“…Important approaches include random-walk and shortest paths based kernels [7,31,4,18], as well as the Weisfeiler-Lehman subtree kernel [30,23]. Further recent works focus on assignment-based approaches [16,27], spectral approaches [15], and graph decomposition approaches [26]. There has been some work considering dynamic graphs.…”

The core decomposition of networks: theory, algorithms and applications

“…In a very recent work [113], the hierarchy of the core decomposition is utilized to provide a general framework for computing similarity metrics among graphs.…”

“…trees, cycles) are compared between graphs in a local or global level with graph kernels. The aforementioned work [113], contributes by utilizing existing kernels at equivalent core levels between graphs in order to compare the structures at similar levels of connectivity.…”