ffstruc2vec: Flat, Flexible and Scalable Learning of Node Representations from Structural Identities

TL;DR

ffstruc2vec addresses the need for scalable node embeddings that preserve structural identities across diverse downstream tasks. It builds a flat similarity graph from multiple graph indicators, learns embeddings via biased random walks and Skip-gram, and then applies task-aware optimization to tailor representations to specific applications. The method delivers greater flexibility, interpretability, and scalability than prior work like struc2vec, with empirical gains on unsupervised and supervised benchmarks across synthetic and real networks. This framework enables explainable reasoning about which structural motifs drive downstream outcomes, making it practical for large-scale graphs in domains such as fraud detection and air-traffic analysis.

Abstract

Node embedding refers to techniques that generate low-dimensional vector representations of nodes in a graph while preserving specific properties of the nodes. A key challenge in the field is developing scalable methods that can preserve structural properties suitable for the required types of structural patterns of a given downstream application task. While most existing methods focus on preserving node proximity, those that do preserve structural properties often lack the flexibility to preserve various types of structural patterns required by downstream application tasks. This paper introduces ffstruc2vec, a scalable deep-learning framework for learning node embedding vectors that preserve structural identities. Its flat, efficient architecture allows high flexibility in capturing diverse types of structural patterns, enabling broad adaptability to various downstream application tasks. The proposed framework significantly outperforms existing approaches across diverse unsupervised and supervised tasks in practical applications. Moreover, ffstruc2vec enables explainability by quantifying how individual structural patterns influence task outcomes, providing actionable interpretation. To our knowledge, no existing framework combines this level of flexibility, scalability, and structural interpretability, underscoring its unique capabilities.

Figures (16)

• Figure 1: ffstruc2vec applied to the mirrored Zachary's Karate Club. Nodes with special structural properties in the graph (upper picture), such as central and peripheral nodes, are marked in color. The ffstruc2vec approach effectively separates the embedding vectors of these nodes from the other nodes (lower picture)
• Figure 2: Visualization of $k$-hop neighborhoods for nodes $x$ and $y$. The neighborhoods are color-coded as follows: green for $k = 1$, blue for $k = 2$, and gray for $k = 3$
• Figure 3: Automorphism orbits $0, 1, 2, \dots, 72$ for the thirty $2$-, $3$-, $4$-, and $5$-node graphlets $G_0, G_1, \dots, G_{29}$. In a graphlet $G_i$ for $i \in \{0,1,\dots,29\}$, nodes belonging to the same orbit are shaded identically Przulj.2007
• Figure 4: Example of a similarity graph $G'$ constructed from the original graph $G$. Nodes with the same structural properties in $G$ are depicted in the same color, while edges with high weights—indicating a high degree of structural similarity between the connected nodes—are represented as thick lines in $G'$
• Figure 5: Generating node sequences (right) using random walks on the similarity graph (left). Structurally similar nodes in the original graph result in similar contexts within the generated sequences, as indicated by the matching colors in the illustrations

Theorems & Definitions (8)

• Definition 1
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• Definition 7
• Remark 1