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Let $G=(V,E)$ be a finite graph where $V$ has $n$ elements so that $V=\{v_1,...,v_n\}$.

Now, define $a_{ij}$ to be 1 if $(v_i,v_j)\in E$ and 0 otherwise. What is this $n\times n$ matrix $(a_{ij})$ called? In some texts, it is defined as an "incidence matrix", but the definition of incidence matrix in wikipedia is not the same.

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This is the adjacency matrix.

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