  In this paper, we prove some combinatorial results on generalized cluster
algebras. To be more precisely, we prove that (i) the seeds of a generalized
cluster algebra $\mathcal A(\mathcal S)$ whose clusters contain particular
cluster variables form a connected subgraph of the exchange graph of $\mathcal
A(\mathcal S)$; (ii) there exists a bijection from the set of cluster variables
of a generalized cluster algebra to the set of cluster variables of another
generalized cluster algebra, if their initial exchange matrices satisfying a
mild condition. Moreover, this bijection preserves the set of clusters of these
two generalized cluster algebras.
  As applications of the second result, we prove some properties of the
components of the $d$-vectors of a generalized cluster algebra and we give a
characterization for the clusters of a generalized cluster algebra.
