I have to go through this paper, where I encountered this definition:
The pattern of a matrix A is a bipartite graph with a node for each row and each column and an edge connecting row node i to column node j whenever $a_{ij} \neq 0$. A matrix B is said, by abuse of language, to have a partial pattern of A if its pattern is a partial graph of the pattern of A (same nodes, subset of the edges). This is equivalent to $a_{ij} = 0 \Rightarrow b_{ij} = 0$. The matrix A is called connected if its pattern is a connected graph. In a graph two nodes are called neighbours if there is an edge connecting them. By abuse of language we extend this terminology to rows and columns (and even row multipliers and column multipliers).
From my understanding i drew this picture:
But I dont seem to get the "by the abuse of language"-Part at the very end. Because in that proof below the author speaks about neighbours of entries of a vector (after the formula). But that matrix/vector-entry cannot have a neighbour, because it is an edge of a graph, which cannot have a neighbor. It makes no sense to me.
