As we saw in this question complex logical statements can be expressed in terms of the simple connectives of generalized Minesweeper. However Generalized minesweeper still has redundancies.
In order to avoid these redundancies we define a new game called "Generalized-1 Minesweeper".
Generalized-1 Minesweeper is a version Minesweeper played on an arbitrary graph. The graph has two types of vertex, an "indicator" or a "value". A value can be either on or off (a mine or a dud) however its state is unknown to the player. An indicator tells that exactly one of the adjacent cells is on (a mine). Indicators do not count as mines themselves.
For example the following board for Generalized Minesweeper tells us that cells A and B are either both mines or neither of them are mines.
(In the diagram indicators are marked in gray while values are white)
Unlike in normal minesweeper where you click values that are off to reveal indicators, there is no such mechanic in Generalized Minesweeper. A player simply determines for what states of the graph can satisfy its indicators.
Your goal is to make a
2 in Generalized-1 Minesweeper.
You will build a structure in Generalized-1 Minesweeper such that there are 8 specific cells for which all possible configurations of values have exactly two cells on. This means it behaves exactly as the
2 does in traditional minesweeper. When you write your solution you should not have specific values in mind for value cells. (In answer to H.PWiz's question it is allowed that some value cells might be deducible from the state)
You answers will be scored by the number of vertices in the final graph minus 8 (for the 8 inputs) with a lower score being better. If two answers tie in this metric the tie breaker will be the number of edges.