Big graph mining is an important research area and it has attracted considerable attention. It allows to process, analyze, and extract meaningful information from large amounts of graph data. Big graph mining has been highly motivated not only by the tremendously increasing size of graphs but also by its huge number of applications. Such applications include bioinformatics, chemoinformatics and social networks. One of the most challenging tasks in big graph mining is pattern mining in big graphs. This task consists on using data mining algorithms to discover interesting, unexpected and useful patterns in large amounts of graph data. It aims also to provide deeper understanding of graph data. In this context, several graph processing frameworks and scaling data mining/pattern mining techniques have been proposed to deal with very big graphs. This paper gives an overview of existing data mining and graph processing frameworks that deal with very big graphs. Then it presents a survey of current researches in the field of data mining/pattern mining in big graphs and discusses the main research issues related to this field. It also gives a categorization of both distributed data mining and machine learning techniques, graph processing frameworks and large scale pattern mining approaches.