A minimum cost spanning tree problem analyzes the way to efficiently connect individuals to a source when they are located at different places. Several rules have been defined to solve this problem. Our objective here is to propose a new approach that differentiates some costs that may deserve compensations (involuntary costs) from some other connection costs that may be considered voluntary. We therefore define a solidarity egalitarian solution, through which, the total cost is allocated by considering pay-backs to equalize the involuntary costs, thus fulfilling the weak stability condition of individual rationality. Keywords: Minimum cost spanning tree, Solidarity, Cost sharing, Egalitarian JEL classification: C71, D63, D71.