# A Distributed Hybrid Community Detection Methodology for Social Networks
## 3 Proposed Methodology  
Due to the social networks rapid growth, the need for eminently efficient and highly scalable methodologies, capable of leveraging all included information modalities, have become very critical. Thus, a novel, distributed community detection methodology is introduced, based on the following intuitive assumptions:  
1. The nodes belonging in the same community are more likely to share common user content attributes, according to the homophily concept [9; 11; 13];
2. The nodes would be assigned to the community where most of their neighbors belong, following the Label Propagation Method concept [3; 10], and the notion of the high intra-connection density prerequisite of Infomap [3]; and
3. The merrier shortest paths that an edge engages, the more probable is to act as interconnection edge between distinct communities, according the [PERSON]'s [8] edge betweenness similarity measure. The proposed methodology is an iterative, divisive community detection process that combines the network topology features of loose similarity and local edge betweenness measure, along with the user content information in order to remove the inter-connection edges and thus unravel the subjacent community structure. Even if this iterative process might sound computationally over-demanding, its application is certainly not prohibitive, since it can be safely concluded from the experimentation results that the aforementioned measures are that well-informative and highly representative, so merely few iterations are required to converge to the final community hierarchy at any case. As shown in Figure 1, initially the preprocessing step takes place. During this phase, the node attribute vectors are constructed regarding each node's intrinsic user content information provided. Then, the cosine similarity [33] calculation between the corresponding vectors of each associated pair of nodes is performed. This calculation can naturally be performed in a distributed fashion and from this point on this similarity metric can be considered as one of the corresponding edge's intrinsic properties. Subsequently, the iteration step is performed. Based on the local clustering concept introduced in [1; 4] and by aligning to the previously defined assumptions, it is more than obvious that the network topology properties of each edge are primarily benefited by their immediate neighbors rather than the whole graph. Therefore, by limiting the network topology measures to the knowledge of the up to a certain depth direct neighbors, both the qualitative clustering and the processing efficiency is ensured. Thus, the network topology properties are expressed as neighbor depth measures where:  
* Regarding an imminent pair of nodes and each of their corresponding sets of distinct k-depth neighbor nodes, the k-depth loose similarity is the fraction of common over the union's total number of nodes. It should be underlined, that both sets might include nodes having depth less or equal to k, since a common node might be at a different depth for each impeding node; and
* The l-depth local edge betweenness of an edge, is the total number of shortest paths that this edge engages focusing on the subgraph containing the up to the l-depth neighbors of its imminent pair of nodes. The difference between the local edge betweenness and the original edge betweenness defined in [8], is that in the latter, the entire graph should be taken under consideration whereas in the proposed methodology this calculation is applied only in an emphatically smaller subgraph, since the repetitive calculation of all possible shortest paths on real-world social networks is considered impossible. So forth, the LS-th depth loose similarity and the EB-th local edge betweenness measures are calculated in each iteration step for each of the existing edges.