A minimum cost spanning tree problem analyzes the way to efficiently connect individuals to a source when they are located at different places; that is, to connect them with the minimum possible cost. This objective requires the cooperation of the involved individuals and, once an efficient network is selected, the question is how to fairly allocate the total cost among these agents. To answer this question the literature proposes several rules providing allocations that, generally, depend on all the possible connection costs, regardless of whether these connections have been used or not in order to build the efficient network. To this regard, our approach defines a simple way to allocate the optimal cost with two main criteria: (1) each individual only pays attention to a few connection costs (the total cost of the optimal network and the cost of connecting by himself to the source); and (2) an egalitarian criteria is used to share costs or benefits. Then, we observe that the spanning tree cost allocation can be turned into a claims problem and, by using claims rules, we define two egalitarian solutions so that the total cost is allocated trying to equalize either the payments in which agents incur, or the benefit that agents obtain throughout cooperation. Finally, by comparing both proposals with other solution concepts proposed in the literature, we select equalizing payments as much as possible and axiomatically analyze it, paying special attention to coalitional stability (core selection), a central property whenever cooperation is needed to carry out the project. As our initial proposal might propose allocations outside the core, we modify it to obtain a core selection and we obtain an alternative interpretation of the Folk solution. Keywords: Minimum cost spanning tree, Egalitarian, Cost sharing, Core. JEL classification: C71, D63, D71.