# Outlier Detection and Prediction in Evolving Communities
## 1 Introduction  
One of the most important parts of social network analysis is community detection, that is, finding highly connected groups of nodes; this important task consists of studying the network and optimizing a function such as modularity to divide nodes into dense sub-networks, called communities. A wide definition of a community remains under discussion in the related literature; the main reason for this is its highly context-dependent nature. The basic idea for describing a community inside a social network is the existence of more intra-community edges than inter-community edges, reflecting more relations between community members than with other nodes outside the group [1, 2]. However, a social network often provides more information about relations of its members in the form of context or semantics. The inclusion of this information through node- or edge-attributed graphs can add important details to the analysis and conclude with more cohesive communities that do not solely rely on structural connections. For example, content information of a co-authorship network could include the conferences, journals, or general subject matter of the published papers, while in an online forum it could include the tags and labels of each post or even the entire post's text. A possible advantage of content inclusion in such cases could be the formation of communities including nodes thatnot only have members exchanging messages between them but share the same context, underlining the group's main topics. A widely discussed drawback of content inclusion in community detection methods is increased complexity [3]. From our point of view, \"semantic connection\" is equally important to structural, as social actors with few links between them and similar content could share the same interests, ideas, or actions. As such, it would be beneficial to include them in the same community. In parallel, one of the most important and continuously rising topics in social networking and data mining, in general, is the search for social actors that can be differentiated from the typical actors' behavior in a network. This procedure is referred to as _outlier detection_ or anomaly detection. In addition to being widely studied in social networks, this has considerable enterprise value. For example, anomaly detection can identify spam posts on review systems when their content follows a different motif than real reviewers' posts. Focusing on social graphs, an outlier is a node that is loosely connected to the rest of the graph and in most cases not a member of any community. Outlier nodes in a social network are often treated as noise, representing, for example, users of social media who rarely interact with others, and who as such have only a few connections with the network and can be excluded from the computations. On the other hand, many interesting applications of outlier detection can be found in the domain of cybersecurity, e.g., fraud detection, as well as in other domains such as advertising. The early detection of outlying nodes can help a company to keep its customers close to its community while trying to attracting other companies' outlying customers through marketing techniques. During our research, we noted a lack of related works on outlier detection with a hybrid approach combining network structure and content. Instead, most outlier detection techniques [4; 5], similarly to community detection ones, rely solely on structural information. In addition, while most real world applications include graphs that change over time, the temporal dimension of the problem is often neglected. Therefore, in this paper we propose a novel algorithm that leverages the dimensions of both content and structure and can perform community detection in dynamic social networks in parallel with outlier detection.