A puzzle built around graphs: sets of nodes joined together by paths. Use with [mathematics]

A graph $G=(V,E)$ consists of a set $V$ of vertices (or nodes) and a set $E$ of edges; every edge in E connects two vertices in V. Two vertices are called adjacent if there is an edge between them.

Graphs are one of the primary objects of study in discrete mathematics and combinatorics. Graph structures often show up in combinatorial puzzles; usually, they are hidden, and part of the solution process is to detect the graph structure. Take note that general graph theory questions are off-topic but can be asked on our sister site Mathematics Stack Exchange using the [graph-theory] tag.