Statistical mechanics of bipartite z-matchings
Eleonora Kreačić, Ginestra Bianconi · Europhysics Letters (EPL) · 2019
The matching problem has a large variety of applications including the allocation of competitive resources and network controllability. The statistical mechanics approach based on the cavity method has shown to be exact in characterising this combinatorial problem on locally tree-like networks. Here we use the cavity method to solve the many-to-one bipartite z -matching problem that can be considered to be a model for the characterisation of the capacity of user-server networks such as wireless communication networks. Finally we study the phase diagram of the model defined in network ensembles.