Problem of finding pairs of elements that co-occur in some number of sets I have a fairly general problem and I wonder if it has a name. The problem statement, as best I can put it, is the following:


  Let $I=\{i_1,i_2,...,i_n\}$ be a set of items. Let $C=\{C_1,C_2,...,C_m\}$ be a set of containers. Each container is unique and contains a set of items from $I$. Let $C_{a,b} \subseteq C$ be the set of containers that contain both $i_a$ and $i_b$. Find all $(i_a, i_b)$ pairs where $\left\vert{C_{a,b}}\right\vert \geq k$ for a given $k \in \mathbb{N}$.


If the items are people and the containers are times and places, then we are asking which people met at least $k$ times. If the items are groceries and the containers are shopping carts, then the problem is a variation of association rule learning. If the items are words and the containers are documents, then we are looking for a co-occurrence network.
You can look into bipartite graphs; the item-set relationships form this type of graph, and the process of clustering highly-connected nodes (loosely speaking) is called community detection (it's similar to frequent itemset mining).