  The present paper deals with some structural properties of transportation
cost spaces, also known as Arens-Eells spaces, Lipschitz-free spaces and
Wasserstein spaces. The main results of this work are: (1) A necessary and
sufficient condition on an infinite metric space $M$, under which the
transportation cost space on $M$ contains an isometric copy of $\ell_1$. The
obtained condition is applied to answer the open questions asked by C\'uth and
Johanis (2017) concerning several specific metric spaces. (2) The description
of the transportation cost space of a weighted finite graph $G$ as the quotient
$\ell_1(E(G))/Z(G)$, where $E(G)$ is the edge set and $Z(G)$ is the cycle space
of $G$. This is a generalization of the previously known result to the case of
any finite metric space.
