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If a differential equation $\\dot x = f(x)$ has a one-dimensional center manifold $W^c$ at an equilibrium $x^*$ then $E^c$ is tangential to $W^c$ with $A = Df(x^*)$ and for stability of $W^c$ it is necessary that $A$ has no spectrum in $\\mathbb{C}^+$, i.e.\\ if $A$ is symmetric, it has to be negative semi-definite.\n  We establish a graph theoretical approach to characterize semi-definiteness. 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If a differential equation $\\dot x = f(x)$ has a one-dimensional center manifold $W^c$ at an equilibrium $x^*$ then $E^c$ is tangential to $W^c$ with $A = Df(x^*)$ and for stability of $W^c$ it is necessary that $A$ has no spectrum in $\\mathbb{C}^+$, i.e.\\ if $A$ is symmetric, it has to be negative semi-definite.\n  We establish a graph theoretical approach to characterize semi-definiteness. 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