If "depreciation" is defined as inflation then a closed form relationship to exchange rates has yet to be determined, but academia generally agrees that if currency A inflates faster than currency B then currency A will drop in price relative to currency B. Even that fact is disputed under certain circumstances.
If it is defined as the phenomenon where the change in a currency's price relative to another currency changes all other exchange rates then it is called "triangular arbitrage".
In a 3 currency universe with currency A, B, and C where each are marketable without restriction, a change in the price of any combination will cause an arbitrage condition among all other possible combinations which in turn forces all combinations back into balance.
For example, If A:B, A:C, and B:C are all initially trading at 1:1, but A:B then trades to 2:1 while the other two remain as they were initially then a potential arbitrage condition arises because 1 B can now buy 2 As, and those 2 As can in turn buy 2 Cs, which can finally buy 2 Bs, allowing a 100% profit in B. Buys and sells will occur in some random fashion to remove this arbitrage condition. This is how an exchange rate involving A can affect a rate that doesn't involve A.
This balancing mechanism can only occur if there are no restrictions on currency trade, but black market exchange rates will almost always maintain equilibrium, the condition where arbitrage is not available.