  Einstein-Podolsky-Rosen (EPR) steering, as one of the most intriguing
phenomenon of quantum mechanics, is a useful quantum resource for quantum
communication. Understanding the type of EPR steering in a graph state is the
basis for application of it in a quantum network. In this paper, we present EPR
steering in a Gaussian weighted graph state, including a linear tripartite and
a four-mode square weighted graph state. The dependence of EPR steering on
weight factor in the weighted graph state is analyzed. Gaussian EPR steering
between two modes of a weighted graph state is presented, which does not exist
in the Gaussian cluster state (where the weight factor is unit). For the
four-mode square Gaussian weighted graph state, EPR steering between one and
its two nearest modes is also presented, which is absent in the four-mode
square Gaussian cluster state. We also show that Gaussian EPR steering in a
weighted graph state is also bounded by the Coffman-Kundu-Wootters monogamy
relation. The presented results are useful for exploiting EPR steering in a
Gaussian weighted graph state as a valuable resource in multiparty quantum
communication tasks.
