In this paper we consider the situation that three identical two-level atoms re sonantly in teract with three distant single-mode optical cavities via a one-photon hopping separately.Three atoms are in like-GHz state and therr optical cavities are all in vacuum state initially.Using the Jaynes-C ummings,the time evolution of the system is given.We adopt the entanglement tensor approach to quantify the degre e of entanglement. The tripartite entanglement dynamics among three atoms and the entanglement dyna mics between two atoms are studied.The influence of atomic states initially on t ripartite entanglement among atoms and two-body entanglement between two atoms are discussed.The results obtained using the numerical method show: first,the time evolution of tripartite entanglement displays the periodic oscill ation behavior and its oscillation period is not realted with the initial degree of entanglement among atmos;second the peak and mean of entanglement measures E₃ and F₂ incease with i ncreasing of the initial degree of entanglement among atmos,which means that the larger the initial degree of entanglement among atoms,the layer the tripartite entanglement among atoms and the two-body entanglement between atoms;third,the phenomenon of sudden death of entanglement between two atoms occurs,and the leng th of the death time interval decreases with increasing of the initial degree of entanglement among atoms.This shows that the length of the death time interval of two-body entanglement can be decreased by selecting initially atomic state w ith high degree of entanglement among atoms.