# Text Semantic Annotation: A Distributed Methodology Based on Community Coherence
## 2 Background
### Community Detection Algorithms
This method's key to success lies in the evaluation of any possible merge of directly connected communities using the modularity function that was formerly used as a quality assessment indicator of the final community structure. Specifically, the modularity similarity function deftly quantifies the concentration of the edges' intra-connecting nodes within a community, opposite to the corresponding nodes' degrees and the potential number of graph's edges, assuming a structure with no edges between the densely connected generated communities. Hence, by originally considering singletons, this greedy approach endeavors to compose meta-communities of communities by merging those for which the generated meta-community's modularity value is close to one, indicating a well-structured community, until no further merging is possible. Despite the fact that its exact computational complexity cannot accurately be calculated, this method seems to run in \(O\)(n logn) time, as regards to the n number of included nodes. A promising alternative to Louvain is the algorithm introduced by [PERSON], [PERSON] and [PERSON] [3]. This heuristic method is also based on the iterative optimization of the modularity similarity function, although differs by:  
* applying some predefined thresholds in the modularity gain on any possible merge,
* excluding all nodes of degree one from the original network and adding them back after the community computation and
* incorporating sophisticated data structures that simplify the hierarchical decomposition of the information network. This method accomplishes the generation of community structures that are fundamentally different from Louvain's extracted hierarchies. Specifically, this algorithm tends to form meta-communities of a large fraction of nodes which have basically lower modularity values compared to the community structures identified by application of the Louvain algorithm. It is worth mentioning that in sparse graphs the computational complexity of this approach is assuredly limited to O(n log\({}^{2}\)n) as regards the n number of nodes included. Finally, inspired by radically different scientific backgrounds, the category of other approaches includes optimization methods that try to approximate this network topology optimization problem from substantially different perspectives. From methods inspired from discrete mathematics and physics, to techniques that project the original community detection definition to conceptually different contexts, the conducted research can certainly be characterized affluent. The most indicative include, but are not limited to, the spectral optimization, the Wu and Huberman algorithm, the Information Diffusion Graph Clustering approach, Simulated Annealing, the Markov chains and random walks optimization algorithm, the genetic algorithms approximation, the External Optimization algorithm, and flow betweenness maximization based on the elementary Kirchhoff circuit theory. However, due to the over-demanding statistical analysis required and the mandatory data representation transformation applied, these are not further discussed and are considered outside the scope of this paper.