  In this letter, we consider the implementation problem of distributed graph
filters, where each node only has access to the signals of the current and its
neighboring nodes. By using Gaussian elimination, we show that as long as the
graph is connected, we can implement any graph filter by decomposing the filter
into a product of directly implementable filters, filters that only use the
signals at the current and neighboring nodes as inputs. We have also included a
concrete example as an illustration.
