Social Mining and Community Finding methods can be seen as a particular application domain of Big Data, Data Mining and Machine Learning areas. The interest in Community Finding Problems on Social Networks (SN) have experienced an increasing attention over the last years due to the straightforward access to the information stored in these sources, which can be done through APIs or bots. Once the information is gathered and pre-processed, is theoretically simple to apply different kind of algorithms to analyse the knowledge structure, extracting patterns that can be later used in Decision Support Systems. However, when this kind of algorithms are applied over some specific domains (e.g. radical networks, polarized networks, etc.), some problems related to both the amount of available and the quality of information, can be a challenge to the application of traditional Machine Learning-based methods. This talk will provide an introduction to some basics on Social Networks Analysis, and some popular algorithms and tools used in the area of Community Finding Detection. The talk will briefly analyse the main challenges and problems related to small SN (networks with low amount of trustworthy data), and how these methods could be applied to extract patterns from static SN (where no modifications are allowed during the application of the algorithm).