Subgraph Structure Feature Learning for Triangle Clique Prediction in Complex Networks

Link prediction is a critical task in network analysis, widely used to infer potential relationships between nodes. While traditional methods focus on pairwise interactions, real-world networks often exhibit higher-order interactions involving multiple nodes, such as 3-clique (triangle), which play a crucial role in understanding tightly-knit groups and complex network dynamics. In this paper, we propose a triangle clique prediction method based on <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><b>S</b></u>ubgraph <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><b>S</b></u>tructure <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><b>F</b></u>eature <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><b>L</b></u>earning (SSFL), which focuses on triangle structures in a network for prediction. In detail, it extracts the one-hop neighborhood around a target 3-clique, encodes it as a enclosing subgraph, and represents its structural features as a vector. These feature vectors are then processed using a fully connected neural network to predict 3-clique formations effectively. Experimental results show that the proposed method outperforms similarity-based link prediction methods and demonstrates comparable performance to embedding-based and machine learning-based approaches across various datasets. Our work can not only directly predict 3-clique structures in a network, but also provides insights into better understanding the evolution mechanism of networks. All source code is publicly available at: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/yabingyao/SSFL4HigherOrderLinkPrediction</uri>.