Before revision:  We show that these constraints preserve two important aspects of credit networks. The first is route independence: if there are multiple trust-paths over which a transaction can clear, then it does not matter which one is used. The second pertains to liquidity (i.e. the fraction of transactions that succeed): given a symmetric transaction matrix, any achievable vector of net "credit balances" of the agents is equally likely. This technical property allows us to extend the original analysis of liquidity in credit networks to the constrained case. Surprisingly, aggregate borrowing constraints greatly simplify the analysis and achieve the optimal tradeoff between liquidity and the number of trust-edges .
After revision:  We show that these constraints preserve the analytical structure of a credit network. Furthermore, we show that aggregate borrowing constraints greatly simplify the analysis and achieve the optimal tradeoff between liquidity and the number of trust-edges .