MSGCN: Multiplex Spatial Graph Convolution Network for Interlayer Link Weight Prediction

TL;DR

The paper tackles interlayer link weight prediction in multiplex networks, a task that benefits from capturing cross-layer structure while respecting node geometry. It introduces MSGCN, which projects node features across layers and applies spatial graph convolution to learn interlayer dependencies, complemented by a custom loss to mitigate oversmoothing. Across synthetic datasets with known interlayer links, MSGCN achieves robust, generalizable predictions and outperforms extended single-layer baselines in accuracy and stability. The work offers practical implications for spatially embedded multiplex systems (e.g., transportation, biology) and outlines avenues for scalability and broader network generalization.

Abstract

Graph Neural Networks (GNNs) have been widely used for various learning tasks, ranging from node classification to link prediction. They have demonstrated excellent performance in multiple domains involving graph-structured data. However, an important category of learning tasks, namely link weight prediction, has received less emphasis due to its increased complexity compared to binary link classification. Link weight prediction becomes even more challenging when considering multilayer networks, where nodes can be interconnected across multiple layers. To address these challenges, we propose a new method named Multiplex Spatial Graph Convolution Network (MSGCN), which spatially embeds information across multiple layers to predict interlayer link weights. The MSGCN model generalizes spatial graph convolution to multiplex networks and captures the geometric structure of nodes across multiple layers. Extensive experiments using data with known interlayer link information show that the MSGCN model has robust, accurate, and generalizable link weight prediction performance across a wide variety of multiplex network structures.

Figures (14)

• Figure 1: Sample spatial multiplex network showing different link and node types between layers.
• Figure 2: Overview of the Multiplex Spatial Graph Convolution Network (MSGCN): The process begins in (a) with a multiplex network where nodes are in the same spatial position across layers. In (b), node features are projected across diagonal links to adjacent layers. Next, in (c), spatial graph convolution is applied to each projected graph. The spatial graph convolution network layers are shown in yellow to distinguish them from the multiplex network layers. Message passing captures the projected node's relationship to it's neighbors. Finally, in (d), the aggregation step from the spatial graph convolution estimates the predicted interlay link weights.
• Figure 3: Details of the data generation method with only a few representative variables labeled in the figure for clarity. In (a) an initial spatial multiplex network is created using the parameters in Table \ref{['tab:graph_parameters']}. Next, in (b) random weights are assigned to each intralayer edge. Then, in (c) random node feature values are assigned to each node. Finally, in (d) node features and interlayer edge weights are updated using equations \ref{['eq:graph_generation']} and \ref{['eq:edge_weights']} to ensure a linear relationships between neighbors and layers.
• Figure 4: Predicted link weights against actual values for all the experiments ran in this study. The results demonstrate the effectiveness of the MSGCN method in predicting unseen interlayer link weights across various network types, network sizes and number of layers.
• Figure 5: A comparison of different interlayer link weight prediction models based on 25 simulated multilayer networks shows that the MSGCN method has significantly higher Pearson correlation values between the predicted values and the ground truth. The p-values correspond to the t-tests that were conducted to compare the means of different groups in the study.