Analysis of Networks in Chess
http://snap.stanford.edu/class/cs224w-2013/projects2013/cs224w-023-final.pdf
This paper pertains to how networks can be used to analyze a chess position. It sets out by defining the chess pieces on each side and explains the calculation of ELO rating points for players. They would like to evaluate board positions using different networks, and ultimately try to predict game outcomes.
The first network that was set up is a support network. This means that there are all the possible nodes as chess pieces. Each node (piece) is connected by an attack edge to a piece that it can capture. This means that if a White Queen on A1 would be be able to capture a Black Rook on A7, the Queen would have an edge to the Rook node. Also, each node (piece) is connected by a defend edge to the piece that it defends. This is when the White Queen on A1 is defending a White Rook on A7.
The second network is a mobility network. Here, every square is a node (for a total of 64 squares). Each node occupied by a piece has the piece name and color on it while unoccupied nodes are blank. Each edge from an occupied node is directed to nodes (or squares) that the piece can reach or capture. Every edge is also assigned the color of the piece.
The third network is the position network which links all the pieces together and is similar to the mobility node. The fifth network is called the tracking network and represents the history of the pieces across the board.
While the paper aims to predict the outcome of the matches, I noticed some similarities between the class material and the paper. For example, the Strong Triadic Closure Property would be seen for a three pieces of the same color. Here, they would be connected, and it’s likely that the other pair would eventually join the support network. Likewise, we can see the Balance Structure property when two attacking pieces of the same color would “target” an enemy piece, as seen on a mobility network.
In all, networks can be used in various instances and analyses of chess as a game.