Graph Similarity Measurement and Analysis in Large Networks

Graph similarity measurement underpins a host of tasks in data science, from detecting communities in social media to aligning multimodal biological networks. Large networks often comprise millions or billions of nodes and edges, rendering exact pairwise comparisons infeasible. Contemporary approaches fall broadly into two categories: topology-based metrics that exploit link patterns, and representation-learning methods that map nodes into compact vector spaces. Topology-based metrics such as SimRank and its variants assess similarity by propagating scores along incoming or outgoing links, capturing structural equivalence and proximity. Embedding techniques, including graph neural networks and random-walk models, learn low-dimensional node vectors that preserve neighbourhood information, enabling efficient similarity queries via simple vector operations. Recent advances tackle challenges posed by heterogeneous and multilayer networks, dynamic edge updates and semantic enrichment. Scalability is achieved through pruning strategies, approximate solvers for linear systems and parallelised computation. Applications span recommendation systems, anomaly detection, network alignment and role discovery. Ongoing work seeks to harmonise the interpretability of topology-based measures with the adaptability of learned embeddings, offering richer insights into evolving large-scale networked systems.

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Graph Similarity Measurement and Analysis in Large Networks publication trend

The graph below shows the total number of articles in graph similarity measurement and analysis in large networks across all publications each year (not limited to Nature Index journals).

Technical terms

Node embedding: A low-dimensional vector representation of a node that preserves its local and global structural properties in the original graph.

SimRank: An iterative topology-based similarity measure defined by the principle that two nodes are similar if their neighbours are similar.

Graph isomorphism network (GIN): A class of graph neural networks designed to distinguish graph structures by learning injective aggregation functions over node neighbourhoods.

Heterogeneous information network (HIN): A graph comprising multiple types of nodes and edges, representing diverse entities and relations in a single framework.

Multilayer network: A network model in which nodes may participate in multiple contexts or layers, each with its own edge set, enabling cross-layer analysis.

References

1. SimRank*: effective and scalable pairwise similarity search based on graph topology. The VLDB Journal (2019).
2. On Investigating Both Effectiveness and Efficiency of Embedding Methods in Task of Similarity Computation of Nodes in Graphs. Applied Sciences (2020).
3. HitSim: An Efficient Algorithm for Single-Source and Top-k SimRank Computation. Information (2024).
4. Fast computation of General SimRank on heterogeneous information network. Discover Computing (2024).
5. PyMulSim: a method for computing node similarities between multilayer networks via graph isomorphism networks. BMC Bioinformatics (2024).