Knowledge mining from single graph plays an important role in decision support systems on single graphs such as social networks, bioinformatics, etc. In recent years, the problem of Frequent Subgraph Mining (FSM) from a single graph have been developed and attracted several studies. However, the problem of mining association rules or links from frequent subgraphs has not had many contributions. In this article, we state the problem of direct mining association rules from frequent subgraphs. Existing approaches on this topic perform the task in two phases. First, they traverse the search space to directly discover parent-child relationships from the discovered frequent subgraphs, then association rules are generated. We propose a one-phase algorithm, named So-GPARs, to generate rules as soon as frequent supergraphs are constructed from already existing frequent subgraphs. Our experiments on three single graph datasets show that the one-phase algorithm is more efficient than the two-phase algorithm in terms runtime of the rules generating phase.

Closed sequential pattern (CSP) mining is an optimization technique in sequential pattern mining because they produce more compact representations. Additionally, the runtime and memory usage required for mining CSPs is much lower than the sequential pattern mining. This task has fascinated numerous researchers. In this study, we propose a novel approach for closed clickstream pattern mining using C-List (CCPC) data structure. Closed clickstream pattern mining is a more specific task of CSP mining that has been lacking in research investment; nevertheless, it has promising applications in various fields. CCPC consists of two key steps: It initially builds the SPPC-tree and the C-List for each frequent 1-pattern and then determines all frequently closed clickstream 1-patterns; next, it constructs the C-List for each frequent k-pattern and mines the remaining frequently closed k-patterns. The proposed method is optimized by modifying the SPPC-tree structure and a new property is added into each node element in both the SPPC-tree and C-Lists to quickly prune nonclosed clickstream. Experimental results conducted on several datasets show that the proposed method is better than the previous techniques and improves the runtime and memory usage in most cases, especially when using low minimum support thresholds on the huge databases.