  In this paper, we study fractional multiflows in undirected graphs. A
fractional multiflow in a graph G with a node subset T, called terminals, is a
collection of weighted paths with ends in T such that the total weights of
paths traversing each edge does not exceed 1. Well-known fractional path
packing problem consists of maximizing the total weight of paths with ends in a
subset S of TxT over all fractional multiflows. Together, G,T and S form a
network. A network is an Eulerian network if all nodes in N\T have even
degrees.
  A term "fractionality" was defined for the fractional path packing problem by
A. Karzanov as the smallest natural number D so that there exists a solution to
the problem that becomes integer-valued when multiplied by D. A. Karzanov has
defined the class of Eulerian networks in terms of T and S, outside which D is
infinite and proved that whithin this class D can be 1,2 or 4. He conjectured
that D should be 1 or 2 for this class of networks. In this paper we prove this
conjecture.
