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The surface structure of a ferrofluid was investigated by means of non-specular X-ray reflection. Strong intensity that is impossible to explain by surface fluctuations due to capillary waves was observed. It can be related to lateral correlation within aggregates of super-paramagnetic fine particles in the vicinity of the specimen surface. The fractal dimension of these surface-induced aggregates and the surface-tension coefficient of the ferrofluid were simultaneously determined. The fractal dimension was found to be around 1.1, indicating a chain-like character of the aggregates that have few branches. Strong and anisotropic interaction among the particles, as well as irreversible aggregation kinetics must be the origin of such a high-density and low-fractal-dimension system of dipolar 10 nm sized particles. The temperature variation of the fractal dimension indicated that the fractal aggregates stabilize themselves by losing their branches at increasing temperatures.