# Detection of core-periphery structure in networks by 3-tuple motifs

## TL;DR

This paper introduces a parameter-free algorithm using 3-tuple motifs to detect core-periphery structures in networks, applicable to large-scale and various types of networks, improving efficiency and flexibility.

## Contribution

The novel contribution is a motif-based, parameter-free method for identifying core-periphery structures in networks, capable of detecting multiple and local structures.

## Key findings

- Effective on synthetic and empirical networks
- Detects multiple and local core-periphery structures
- Efficient and scalable to large networks

## Abstract

Recently, the core-periphery (CP) structure of networks as one type of meso-scale structure has received attention. The CP structure is composed of a dense core and a sparse connected periphery. In this paper, we propose an algorithm to detect the CP structure based on the 3-tuple motif, which is inspired by the idea of motif. In this algorithm, we first define a 3-tuple motif by considering the property of nodes, and then a motif adjacency matrix is formed based on the defined motif, finally, the detection of the CP structure is converted to find a cluster that minimizes the smallest motif conductance. Our algorithm can detect different CP structures: including single or multiple CP structure; and local or global CP structures. Results in the synthetic and the empirical networks indicate that the method is efficient and can apply to large-scale networks. More importantly, our algorithm is parameter free, where the core and periphery are detected without the need for any predefined parameters.