For integers
m >
r ≥ 0, Brietzke (2008) defined the (
m,
r)-central coefficients of an infinite lower triangular matrix
G = (
d,
h) = (
dn,k)
n,k∈N as
dmn+r,(m?1)n+r, with
n = 0, 1, 2,..., and the (
m,
r)-central coefficient triangle of
G as
$${G^{\left( {m,r} \right)}} = {\left( {{d_{mn + r,\left( {m - 1} \right)n + k + r}}} \right)_{n,k \in \mathbb{N}}}.$$
It is known that the (
m,
r)-central coefficient triangles of any Riordan array are also Riordan arrays. In this paper, for a Riordan array
G = (
d,
h) with
h(0) = 0 and
d(0),
h′(0) ≠ 0, we obtain the generating function of its (
m,
r)-central coefficients and give an explicit representation for the (
m,
r)-central Riordan array
G(m,r) in terms of the Riordan array
G. Meanwhile, the algebraic structures of the (
m,
r)-central Riordan arrays are also investigated, such as their decompositions, their inverses, and their recessive expressions in terms of
m and
r. As applications, we determine the (
m,
r)-central Riordan arrays of the Pascal matrix and other Riordan arrays, from which numerous identities are constructed by a uniform approach.