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Graph clustering is a fundamental problem in social network analysis, the goal of which is to group vertices of a graph into a series of densely knitted clusters with each cluster well separated from all the others. Classical graph clustering methods take advantage of the graph topology to model and quantify vertex proximity. With the proliferation of rich graph contents, such as user profiles in social networks, and gene annotations in protein interaction networks, it is essential to consider both the structure and content information of graphs for high-quality graph clustering. In this paper, we propose a graph embedding approach to clustering content-enriched graphs. The key idea is to embed each vertex of a graph into a continuous vector space where the localized structural and attributive information of vertices can be encoded in a unified, latent representation. Specifically, we quantify vertex-wise attribute proximity into edge weights, and employ truncated, attribute-aware random walks to learn the latent representations for vertices. We evaluate our attribute-aware graph embedding method in real-world attributed graphs, and the results demonstrate its effectiveness in comparison with state-of-the-art algorithms.
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Representing Higher-Order Networks with Spectral Moments
The spectral properties of traditional (dyadic) graphs, where an edge connects exactly two vertices, are widely studied in different applications. These spectral properties are closely connected to the structural properties of dyadic graphs. We generalize such connections and characterize higher-order networks by their spectral information. We first split the higher-order graphs by their “edge orders” into several uniform hypergraphs. For each uniform hypergraph, we extract the corresponding spectral information from the transition matrices of carefully designed random walks. From each spectrum, we compute the first few spectral moments and use all such spectral moments across different “edge orders” as the higher-order graph representation. We show that these moments not only clearly indicate the return probabilities of random walks but are also closely related to various higher-order network properties such as degree distribution and clustering coefficient. Extensive experiments show the utility of this new representation in various settings. For instance, graph classification on higher-order graphs shows that this representation significantly outperforms other techniques.
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- Award ID(s):
- 1942929
- PAR ID:
- 10639025
- Publisher / Repository:
- Springer Nature Singapore
- Date Published:
- Page Range / eLocation ID:
- 211 to 223
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Book Chapter:
- https://doi.org/10.1007/978-981-96-8173-0_17
