# Uncovering Hidden Community Structure in Multi-Layer Networks
## 1 Introduction  
Uncovering community structures of a complex network can help us to understand how the network functions. On the other hand, finding communities and then attempting to analyze them is a compelling approach to understand all kinds of network organization structures and their functions. These communities often correspond to some functional units. Over the past decades, the problem of finding community has received significant research attention in the field of network analysis, as it can reveal information about the network structure and the flow of information throughout the network [1]. Community detection is substantial for multiple reasons, including node classification which involves homogeneous clusters, group leaders or crucial group connectors. Communities may be associated with groups of pages of the World Wide Web dealing with related topics [2]. Early work focused primarily on identifying disjoint communities that partition the set of nodes within a network [3, 4]. More recently, researchers have observed the multiplicity of interwoven memberships of communities and have developed algorithms for finding overlapping communities [5, 6]. However, there are several techniques that have been extended to solve other problems in the same field of community detection. One critical issue, which has been extensively studied in the literature since the early analysis of complex networks, is the identification of communities or relationships hidden within the structure of these networks. Considering the domain of community detection, there is another community structure known as the hidden community structure, which is gradually becoming a hot topic of research. For the hidden communities, there is hidden community detection, which aims to identify the invisible community structure in the network that often goes undetected or ignored by many popular community detection algorithms. In the same way, many real-world networks contain scarce community structures,: for example, secret groupsor organizations, which are considered inadequate compared to the dense community structure in particular families, colleagues, or close friends, as calculated by distinguished community scoring metrics. If the members in the less modular community also reside in other, denser communities, then the community is usually omitted. As illustrated in Figure 1, for a small network, the hidden community structure is sparser, and it is perplexed with the structure of the dominant communities making it challenging for algorithms to detect. Moreover, as the networks can be comprised of not only a single layer but several layers, there is a possibility to have some hidden weaker overlapping community structure in them as well. However, multi-layer network models provide a vigorous and more realistic tool for the analysis of many complex systems and networks [7]. For instance, in many social networks, a person can have multiple social accounts across certain social networks and it has also, at present, become foremost to link distributed user profiles which belong to the same person from various platforms. Relationships among those accounts on different social platforms might include online as well as offline ties, such as account following, like/comment interactions, working rela-tionships, hangouts relationships, etc. Such scenarios can effectively be represented using a multi-layer network model. As the concept of this paper is about the detection of hidden communities in networks with a dense structure comprised of multiple layers, there is a possibility that these structures have some weaker communities as well that often go undetected due to the presence of stronger communities. This paper aims to analyze the hidden community structure through a hidden community detection (HCD) algorithm applied and observed in real-world networks to answer the question of whether the real-world networks have hidden community organization or not.