NOVELTY - Forming a vapor-grown graphite fibers (VGGF) composition, comprises: (a) preparing a liquid raw material by mixing a hydrocarbon compound, a transition metal compound catalyst and a co-catalyst mixture comprising a coordinating ligand containing a keto-enol tautomerism, organic compound containing polysulfide group and a bicyclic organic compound containing nitrogen; (b) vaporizing the liquid raw material; (c) introducing the raw material gas and hydrogen gas into a tubular reactor to perform a pyrolysis reaction; and (d) performing a high-temperature graphitization treatment on the VGCF.    USE - The method is useful for forming a VGGF composition, which is useful: in a mixture (claimed) used in a lithium ion battery electrode material, a fuel cell material, an electrically-conductive composite material, a thermally-conductive composite material and a composite material with mechanical strength; and as an additive for manufacturing a fuel cell bipolar plate and for a positive electrode active material for manufacturing a coin cell.    ADVANTAGE - The in-situ method simply and rapidly produces the VGGF composition with three-dimensional linkage structure, and reduced the detrimental effect of impurities (non-fibrous carbon, water content and metal content) thus greatly increasing the number of networks in the composite material and improving the electrical and thermal conductivities and strength of the composite material. The composition promotes the power and cycle life of the battery.    DETAILED DESCRIPTION - Forming a vapor-grown graphite fibers (VGGF) composition, comprises: (a) preparing a liquid raw material by mixing a hydrocarbon compound, a transition metal compound catalyst and a co-catalyst mixture comprising a coordinating ligand containing a keto-enol tautomerism, an organic compound containing a polysulfide group, and a bicyclic organic compound containing nitrogen; (b) vaporizing the liquid raw material to form raw material gas; (c) introducing the raw material gas and hydrogen gas into a tubular reactor for performing a pyrolysis reaction to produce a vapor-grown carbon fibers composition having pure carbon fibers with three-dimensional (3-D) linkage structures; and (d) performing a high-temperature graphitization treatment on the VGCF to form the VGGF composition. INDEPENDENT CLAIMS are included for:    (1) the VGGF composition comprising a carbon ingredient containing a carbon content of at least 99.9 wt.%, and non-fibrous carbon, where the carbon ingredient has a graphitization degree of at least 75% and comprises fibrous VGGF comprising graphite fibers having 3-D linkage structures, the content of the graphite fibers having the 3-D linkage structure in the fibrous VGGF measured by a scanning electron microscopy (SEM) is 5-50 area%, an area ratio of the non-fibrous carbon to the fibrous VGGF measured by the SEM is less than or equal to 5%; and    (2) a mixture comprising a rubber, a plastic, a metal oxide or a carbon material, and the VGGF composition.