Topological motifs populate complex networks through grouped attachment

Jaejoon Choi,Doheon Lee

doi:10.1038/s41598-018-30845-4

Jaejoon Choi, Doheon Lee

Open Access

https://doi.org/10.1038/s41598-018-30845-4

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Abstract

Network motifs are topological subgraph patterns that recur with statistical significance in a network. Network motifs have been widely utilized to represent important topological features for analyzing the functional properties of complex networks. While recent studies have shown the importance of network motifs, existing network models are not capable of reproducing real-world topological properties of network motifs, such as the frequency of network motifs and relative graphlet frequency distances. Here, we propose a new network measure and a new network model to reconstruct real-world network topologies, by incorporating our Grouped Attachment algorithm to generate networks in which closely related nodes have similar edge connections. We applied the proposed model to real-world complex networks, and the resulting constructed networks more closely reflected real-world network motif properties than did the existing models that we tested: the Erdös–Rényi, small-world, scale-free, popularity-similarity-optimization, and nonuniform popularity-similarity-optimization models. Furthermore, we adapted the preferential attachment algorithm to our model to gain scale-free properties while preserving motif properties. Our findings show that grouped attachment is one possible mechanism to reproduce network motif recurrence in real-world complex networks.

Highlights

Researchers have developed network models for real-world systems such as protein-protein interactions (PPIs), author collaborations, the World Wide Web (WWW), and social networks in order to analyze the relationship between the functions and structures in those real-world systems
While recent studies have shown the importance of analyzing network motifs and graphlets[20,21,22,23,24,25], current network models are not capable of reproducing real-world topological properties of network motifs
This result shows that previous network models have quite different network motifs from the real network, and our proposed model networks have higher network motif similarity to the real network compared to other network models

Summary

Introduction

Researchers have developed network models for real-world systems such as protein-protein interactions (PPIs), author collaborations, the World Wide Web (WWW), and social networks in order to analyze the relationship between the functions and structures in those real-world systems. The three classic models for describing real-world properties are the Erdös–Rényi (ER)[1], small-world (SW)[2], and scale-free (SF)[3] models. Two hyperbolic geometrical models have been developed: popularity-similarity-optimization (PSO)[7], and nonuniform popularity-similarity-optimization (nPSO)[8,9] models These models have been proved to be able to reproduce real-world properties such as clustering, small-worldness, power-lawness, rich-clubness and community structure[8,10,11]. Various studies on topological measures of networks have highlighted the importance of network motifs and graphlets in analyzing real-world networks properties, including scale-free, geometric, complex, or high-order networks[13,14,15,16,17,18,19].

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