# An Information-Theoretic Approach for Detecting Community Structure Based on Network Representation
## 1 Introduction  
A network topology diagram (or network diagram for short) is an abstract representation of systems and structures that commonly exist in the real world. In a network diagram, a node represents an individual or element in the system, and an edge represents the relationship between individuals or elements. It has been shown that some nodes in the network are more closely connected to each other than to the other parts of the network, and therefore these nodes can be regarded as an independent part, called a community [1]. Community structures reflect the local topological features and the relationships between elements. Thus, detecting communities in a network diagram becomes an indispensable step in understanding the maintenance and evolution of a network, and this can be applied to the analysis and prediction of the real-world network systems. For example, constructing a recommendation system on the basis of the community detection of friend relationship networks and identifying advertising marketing behaviors and telecom frauds by detecting abnormal links between communities in a telecommunication network [2]. However, finding the community structure accurately in the network has been proven to be a difficult task. This is mainly due to two reasons, one being the ambiguity definition of the pros and cons of a community, and the other being that there are an exponentially large number of possible community partitions [1]. For the former, although researchers generally reach a consensus that a community is a cluster of nodes with closer internal connections than external connections, different researchers use different indexes to define and measure this closeness, including the well-known modularity. However, these indexes cannot be accurate in all cases. For example, modularity has a resolution limit problem,meaning that in some cases, multiple small communities may be unreasonably identified as one large community. Moreover, there is an exponentially large number of possible community partitions for a network, which makes it impossible to find the optimal by traversing all community partitions under the current computing power. Researchers are trying to find the best partition in a limited search space through various methods of transforming a partition, but there is no guarantee of finding the optimal one. Aiming at these two aspects, a typical community detection algorithm usually includes two parts: one is a community evaluation index, such as modularity, used to evaluate the quality of community partition; the other is a certain method, such as top-down split in GN [3] and LFM algorithms [4], constantly changing the community partition and trying to obtain the maximum value of the community evaluation index. However, for the former, the community evaluation indexes used by the existing algorithms are still inaccurate, which makes the results obtained by these algorithms sets far from ground truth on many real-world datasets. For the latter, the search space of the algorithm is too large, and thus the algorithm cannot efficiently find the optimal community, and sometimes even falls into a local optimum. In recent years, researchers have devoted more attention to studying how to extract the structural information of networks by means of network representation learning, as well as the relationship between the vectorial representation and the original structure of the network. Work in this area includes using community labels to improve network representation algorithms [5; 6], as well as using network representation to improve the accuracy of community detection [6]. Inspired by these studies, we propose a new approach, AMI-NRL. The main idea is to simulate the evaluation process of communities in the real world by network representation learning (NRL) and clustering, then trying to find the most stable state in the process, under the guidance of the community evaluation index on the basis of average mutual information (AMI). The stable state will be output as the result of community detection.