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

Table 6

Description of determinePlayersOnShortestPaths() method.

Line	Description
1-4	This part of the method sets the values of the frequency of the appearance of a player on a shortest path for itself .
	When current player is not source player and the number of shortest paths (size of set ) from the current player to the target is greater that one, Line 3 sets the value of to . The player is already considered on the shortest paths by the neighboring player which called it. Therefore, to prevent double consideration of the player we decrease the value of by one. 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).
5-9	This part of the method sets the values of the frequency of the appearance of a the neighboring players that form the shortest path on the shortest path between players and () and routes the message via the neighboring players forming the shortest paths.
	Line 7 sets the value of for the neighboring player to one because the player is on the shortest path from to .
	Player can only update the values of for its neighboring players, but the frequency of appearance of a player on the shortest paths should be updated for all of the players on the shortest paths between source player and target player . The method calls itself to route the message via its neighboring player and update the values recursively.