The structure of the fluid carbon phase in the pressure region of the graphite, diamond, and BC8 solid phase is investigated. We find increasing coordination numbers with an increase in density. From zero to $30$ GPa, the liquid shows a decrease of packing efficiency with increasing temperature. However, for higher pressures, the coordination number increases with increasing temperature. Up to $1.5$ eV and independent of the pressure up to $1000$ GPa, a double-peak structure in the ion structure factors exists, indicating persisting covalent bonds. Over the whole pressure range from zero to $1000$ GPa, the fluid structure and properties are strongly determined by such covalent bonds.
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