## Source Networks in Chess

http://snap.stanford.edu/class/cs224w-2013/projects2013/cs224w-023-final.pdf

Networks are omnipresent in chess.  In “Analysis of Networks in Chess”, the Stanford team discuss the various areas networks are applicable in chess.  The type of network that interested me the most was support networks. Support networks “represent relationships between pieces.”  They are directed networks which indicate which pieces can attack other pieces, and which pieces can defend other pieces.

In a support network, we treat one piece as the “source piece” and analyze the support network with respect to this piece.  This is similar to the ego network we studied in class, the source piece can be considered an ego. We then analyze the relationship that the other pieces have with respect to the “source piece”.   If some piece A can attack the source piece, then there is a negative edge directed from piece A to the source piece. If some piece B can defend the source piece, then there is a positive edge from piece B to the source.  If there are equal or more positive edges than negative edges, the piece is well protected. However, if there are more negative edges than positive edges, the piece will likely be captured (killed). If we analyze a position in a chess game by mentally sketching out the support network for each piece in the game, we can strategize our next move by figuring out which pieces are vulnerable to capture (getting killed).

For example let’s look at the following diagram (blue edges are negative while orange edges are positive):

In this diagram, the pawn circled in red is likely to be captured.  It has 3 negative edges directed towards it but only 2 orange edges protecting it.

In the next diagram, the knight circled in red is well protected.  Although it has a blue negative edge attacking it, it is protected by the orange edge originating from the white pawn.

Sketching out the source network for each piece in this position will give us an idea of the best move to play.  In this case, white should probably protect its white pawn on d4.  Analyzing these source networks may not only be useful to chess players, but may also be beneficial to chess software developers.