Subgraph Support in a Single Large Graph

Abstract

Abstract-Defining the support (or frequency) of a subgraph is trivial when a database of graphs is given: it is simply the number of graphs in the database that contain the subgraph. However, if the input is one large graph, an appropriate support definition is much more difficult to find. In this paper we study the core problem, namely overlapping embeddings of the subgraph, in detail and suggest a definition that relies on the non-existence of equivalent ancestor embeddings in order to guarantee that the resulting support is anti-monotone. We prove this property and describe a method to compute the support defined in this way.

Efficient Graph Sequence Mining Using Reverse Search

“…The method proposed in this paper efficiently enumerates all rFTSs from a set of graph sequences, whereas the methods in [4], [5] mine all frequent patterns from a long graph sequence. In [9], [17], it is shown that the principle of growing possible patterns can be distinguished from the principle of counting support values of the patterns. Therefore, the proposed method in this paper can be extended to mine rFTSs from a long and large graph sequence based on [9], [17].…”

“…In [9], [17], it is shown that the principle of growing possible patterns can be distinguished from the principle of counting support values of the patterns. Therefore, the proposed method in this paper can be extended to mine rFTSs from a long and large graph sequence based on [9], [17]. By extending our method to mine from graph sequences, we plan to compare the performance of our method with that of Berlingerio's recently proposed method.…”

Incremental Frequent Subgraph Mining on Large Evolving Graphs

“…S 2 has 8 embeddings, which is more than those of S 1 ; therefore, the used metric is not anti-monotonic. Several antimonotonic support metrics have been proposed for mining a single graph such as MIS [13], HO [27] and MNI [28]. MNI is the most efficient, since the computation of MIS and HO is NP-complete, while MNI is linear to the number of embeddings.…”

“…In transactional mining, given a subgraph S, the support of S is simply defined as the number of graphs containing S. On the contrary, single graph mining requires more sophisticated metrics. Several anti-monotone support metrics were proposed for the single graph setting [13], [27], [28]. Compared to our work, most of the existing solutions for both settings focus on static graphs.…”

A Parallel Approach for Frequent Subgraph Mining in a Single Large Graph Using Spark

“…For example, in Figure 1a, the single node graph REF (Refugee) appears three times, while its supergraph REF 3 −GOV appears four times. Without the DCP, the search space cannot be pruned and the exhaustive search is unavoidable [30]. To address this issue, we employ the minimum image (MNI) based support which is anti-monotonic introduced in [31].…”