If two Strong Links (also see note at the bottom of this page) share a common Cell, we can form a Chain of three Cells with the common Cell in the middle. If we assume that the candidate in the Cell at one end of the Chain is not the solution for that Cell, then it must be the solution for the next Cell in the Chain because of the definition of a Strong Link. This, in turn and for the same reason, implies that the candidate can not be the solution for the third Cell in the Chain.

Conversely if we assume that the candidate in the Cell at one end of the Chain is the solution for that Cell, then it can not be the solution for the middle Cell and it must be the solution in the other end Cell of the Chain.

If we consider a longer Chain exclusively made of Strong Links, the successive Nodes alternate from one state to the other.

This strategy analyzes such chains and uses colors to display these states (hence its name). Because there are only two possible states for a candidate, all candidates with the same color must simultaneously be the solution or can not be the solution.

SIMPLE COLORING (TWICE IN A UNIT) : if two Nodes in the Chain belong to the same region (Row, Column or Square) and if they have the same color, then this color can not be the solution because a candidate can not be the solution for two cells in the same region; all candidates with this color can be eliminated. Hence the other color is the solution.

In this example candidate 9 has twice the yellow color in Row "D". If cells in yellow identified the solution then candidate 9 would be the solution in two cells of Row "D", which is not possible. Hence no candidates colored in yellow can be the solution in their respective cells. If the yellow state is not the solution, then the green state is the solution.

SIMPLE COLORING (SEES TWO DIFFERENT COLORS) : as one color must be the solution, a candidate that sees two candidates of different colors that do not see each other is eliminated by one of them (we do not know yet by which one).

In this example candidate 5 in B1 sees a blue candidate 5 in B6 and a pink candidate 5 in H1. One of the two latters is the solution for its cell which eliminates candidate 5 in B1.

NB: more formally, a Strong Link is the relationship that exists between two Cells in a region (Row, Column or Square) when these two Cells are the only Cells in that region that contain a particular candidate: if the candidate is not the solution for the first Cell, then it must be the solution for the second Cell, and vice-versa.
However, in the Chaining Strategies, we consider Strong Links as links going from a Cell or a group of Cells where we assert the candidate is not the solution (we say the candidate is in the "OFF" state) to a Cell or a group of Cells where it then must be the solution (we say the candidate is in the "ON" state).
If we consider a Bi-Value Cell, asserting that one of its candidates is not the solution implies that the other candidate must be the solution. Hence there also exists a Strong Link between the two candidates of a "Bi-Value" Cell.

A Weak Link as a link going from a Cell/group of Cells where the candidate is "ON" to a Cell/group of Cells where it is "OFF".

You can practice this strategy by installing the SudokuCoach application on your Android™ device.