# Detecting the Structural Hole for Social Communities Based on Conductance-Degree
## 1 Introduction  
We are living in an online era, and many people are surfing online social networks to make friends, study, do academic research, or engage in other activities to satisfy their social needs at different levels. Scholarly data can be easily accessed. More powerful data analysis technologies must be developed. The interconnectedness of individuals in different communities has a significant impact on the lifespan and sustainability of the community [1; 2]. The structure that acts as a bridge or tie between individuals of different communities tends to allow access to a richer supply of information and determines whether to allow the information from one group to diffuse to another; therefore, it is important to detect structural holes. [PERSON] [3], who studied the social structures of many organizations, first provided the notion of structural holes as a means to bridge diverse groups and lead to benefits and termed the vertices lying on those positions as structural hole spanners. In social networks, users who bridge different communities are known as structural hole spanners. Structural holes are fundamental in many applications, and several models have been developed [4; 5; 6]. In viral marketing, structural holes can accelerate new product marketing to different groups [7; 8]. Discovering the structural holes from real large-scale networks accurately and efficiently is a challenge that has attracted the attention of researchers.  
There are many models that detect structural holes. However, the nodes identified by the existing model in the social network are not necessarily occupants of the structural hole spanner, but may alsobe the central node of the network. In Figure 1, the larger blue node is a typical structural hole spanner, while the larger yellow node is not a structural hole spanner but has similar more specific features. It is necessary for us to detect the structural holes more accurately and remove the core nodes from the results.  
In this paper, our contributions are as follows:  
1. We present a model called the Conductance-Degree structural hole detection algorithm (CD-SHA), which uses conductance and degree to detect structural holes and uses conductance to detect the local minimum communities (LMCs)
2. We propose an improved label propagation algorithm based on conductance (C-LPA) to recognize communities in a network and filter the structural hole results.  
We use real datasets to evaluate the performance using evaluation indicators, such as constraint, effective size, efficiency, clustering coefficient, and hierarchy. Experimental results show that the structural holes detected by the algorithm act as a bridge between communities in real large-scale social networks. Additionally, the evaluations show that the algorithm performs well regarding accuracy and robustness.  
The remaining parts of this paper are arranged as follows. Section 2 discusses related studies and introduces basic notations. Section 3 proposes a solution to the problem. Section 4 introduces the dataset, and then analyzes and evaluates the performance and results of the algorithm. Section 5 presents the study's conclusions.