The p-facility Huff location problem aims at locating facilities on a competitive environment so as to maximize the market share. While it has been deeply studied in the field of continuous location, in this paper we study the p-facility Huff location problem on networks formulated as a Mixed Integer Nonlinear Programming problem that can be solved by a branch-and-bound algorithm. We propose two approaches for the initialization and division of subproblems, the first one based on the straightforward idea of enumerating every possible combination of p edges of the network as possible locations, and the second one defining sophisticated data structures that exploit the structure of the combinatorial and continuous part of the problem. Bounding rules are designed using DC (difference of convex) and Interval Analysis tools. In our computational study we compare the two approaches on a battery of 21 networks and show that both of them can handle problems for p <= 4 in reasonable computing time. (C) 2016 Elsevier B.V. All rights reserved.