Most existing popular methods for learning graph embedding only consider fixed-order global structural features and lack structures hierarchical representation. To address this weakness, we propose a novel graph embedding algorithm named GraphCSC that realizes classification based on skeleton information using fixed-order structures learned in anonymous random walks manner, and component information using different size subgraphs. Two graphs are similar if their skeletons and components are both similar, thus in our model, we integrate both of them together into embeddings as graph homogeneity characterization. We demonstrate our model on different datasets in comparison with a comprehensive list of up-to-date state-of-the-art baselines, and experiments show that our work is superior in real-world graph classification tasks.

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