A Privacy Preserving Approach to Collaborative Systemic Risk Identification: The Use-Case of Supply Chain Networks

Table 5

Description of the calculateNumberOfShortestPaths () method.

Line	Description
1-11	This part of the method sets the number of the shortest paths () when the current player is the source player .
3-6	This part of the method sets the number of the shortest paths () when the target player is a neighboring player of source player .
	If target player is a neighboring player of source player s (Line 3), Line 5 sets the number of the shortest paths to one () because there is only one shortest path between two neighboring players in an unweighted graph.
7-10	This part of the method sets the number of the shortest paths () when the target player is not a neighboring player of source player .
	If target player is not a neighboring player of source player s, the size of set (that includes all neighboring players which connect current player as source to the target) is the number of shortest paths between player and the target (). As already mentioned, the player has a portion of this value from its own perspective. The final value of is the sum of the decentrally calculated values of all players as shown in Equation (5).
12-15	This part of the method sets the number of the shortest paths () when the current player is not the source player . This player received the request of calculateNumberOfShortestPaths(s,t) because it is one of the players which is forming the shortest path between source and target player.
	Already one of the shortest paths on which the player lies, is considered by the source player . Consequently, we need to consider the additionally identified shortest paths via this player. If there is an additional path via this player to the source, Line 14 sets the value of to , otherwise set it to zero. We decrease the value of by one, to prevent double consideration of the already considered path.
16-19	To consider additional shortest paths which might be identified by the players which are forming the shortest paths between the source and target player, the method recursively routes the message for calculating the number of shortest paths via the neighboring players which are forming the shortest paths (Line 18). The method identifies this neighboring player by Line 16, when .