[Paper Review] Role-similarity based comparison of directed networks

Kathryn Cooper, Mauricio Barahona|arXiv (Cornell University)|Mar 29, 2011

Complex Network Analysis Techniques3 citations

TL;DR

This paper introduces a role-similarity measure for comparing nodes across directed networks by analyzing their in- and out-path flow profiles using weighted adjacency matrix powers. The method enables cross-network node similarity and network structure comparison via graph partitioning of similarity matrices, demonstrating high accuracy in identifying functionally equivalent nodes and structurally similar networks, especially in metabolic and ecological systems.

ABSTRACT

The widespread relevance of complex networks is a valuable tool in the analysis of a broad range of systems. There is a demand for tools which enable the extraction of meaningful information and allow the comparison between different systems. We present a novel measure of similarity between nodes in different networks as a generalization of the concept of self-similarity. A similarity matrix is assembled as the distance between feature vectors that contain the in and out paths of all lengths for each node. Hence, nodes operating in a similar flow environment are considered similar regardless of network membership. We demonstrate that this method has the potential to be influential in tasks such as assigning identity or function to uncharacterized nodes. In addition an innovative application of graph partitioning to the raw results extends the concept to the comparison of networks in terms of their underlying role-structure.

Motivation & Objective

• To develop a generalizable method for comparing node roles across different directed networks based on directional flow structure.
• To extend the concept of self-similarity to inter-network node similarity, enabling functional assignment to uncharacterized nodes.
• To enable comparison of entire network structures by analyzing the underlying role-structure through graph partitioning of similarity matrices.
• To validate the method on real-world networks such as metabolic, foodweb, and world trade networks, showing high structural fidelity in surrogate models.

Proposed method

• The method computes feature vectors for each node using powers of the adjacency matrix and its transpose, capturing incoming and outgoing paths of all lengths up to K.
• It employs a scaling parameter β = α/λ₁, where λ₁ is the largest eigenvalue of the adjacency matrix, to balance local (short paths) and global (long paths) influence.
• Node similarity is computed as the cosine distance between normalized feature vectors derived from these path counts.
• The resulting similarity matrix is used to compare entire networks by applying graph partitioning to reveal underlying role-structure.
• Surrogate networks are generated by preserving group flow proportions and sizes, enabling comparison with original and random networks.
• Maximum mutual information scores are used to quantify similarity between network models, with block-averaged simplifications for visualization.

Experimental results

Research questions

• RQ1 Can node similarity across different directed networks be meaningfully quantified based on their directional flow profiles?
• RQ2 To what extent does the proposed similarity measure correlate with biological or functional equivalence in real-world networks?
• RQ3 Can graph partitioning of similarity matrices reveal and compare the underlying role-structure of different networks?
• RQ4 How do surrogate networks with identical flow structure but random internal connections compare to original and random networks in similarity metrics?

Key findings

• The method successfully identifies functionally equivalent nodes across different networks, with higher similarity scores observed between known homologous metabolites in metabolic networks.
• Surrogate networks preserving group flow structure showed significantly higher similarity to the original network and to each other than to completely random networks with the same size and edge count.
• Networks generated under the same model—such as the niche model, St. Marks foodweb, and world trade network—demonstrated high mutual similarity in their underlying role-structure.
• Metabolic network models (mmu, eco, pai) displayed strong internal similarity, distinct from foodweb and random network models.
• Random directed networks showed no discernible structure and were dissimilar to all other network types, confirming the method's sensitivity to meaningful topology.
• The block-averaged mutual information matrix revealed clear clustering of network types, validating the method’s ability to distinguish structural regimes.