Vertical Memristive Crossbar Array for Multilayer Graph Embedding and Analysis

Graph data structures effectively represent objects and their relationships, enabling the modeling of complex connections in various fields. Recent work demonstrate that metal at diagonal crossbar arrays (m-CBA) can effectively represent planar graphs. However, they are unsuitable for representing multilayer graphs having multiple relationships across different layers. Using conventional software, embedding multilayer graphs in high-dimensional Euclidean spaces introduces significant mathematical complexity and computational burden, often resulting in information loss. This study proposes a unique graph embedding (mapping) method utilizing a fabricated vertical m-CBA (vm-CBA), where a custom-built measurement system thoroughly validated its functionality. This structure directly maps multilayer graphs into a 3D vm-CBA, accurately representing inter-layer and intra-layer connections. The practical link prediction and information scores across various real-world datasets demonstrated that vm-CBA achieved enhanced accuracy compared to conventional embeddings, even with a significantly decreased number of operations.