设$\{{\xi }_i{\}}_{i=1}^{\mathrm{\infty }}$是一列独立同分布在图$\mathit{\Gamma }=(V(\mathit{\Gamma }),E(\mathit{\Gamma }))$上取值的随机元, $\{a_i{\}}_{i=1}^{\mathrm{\infty }}$是一列固定 的正整数. 文章给出图值随机元序列的$r$-阶权函数、$r$-阶均值集与$r$-阶中心序等概念, 将随机元序列的Fr\'{e}chet样本均值的概念推广到更一般的情形, 并且讨论了其基本性质, 获得了关于图值随机元序列的广义强大数定理.

Let $\{{\xi }_i{\}}_{i=1}^{\mathrm{\infty }}$ be a sequence of independent identically distributed random elements taking values on a graph $\mathit{\Gamma }=(V(\mathit{\Gamma }),E(\mathit{\Gamma }))$, $\{a_i{\}}_{i=1}^{\mathrm{\infty }}$ be a sequence of fixed positive integers. In this paper, we first give the definitions of general $r$th weight function, $r$-th order mean set and $r$-th cental order of random elements. Then, we extend the Fr\'{e}chet mean of random elements to more generalized cases and discuss some basic properties of them. Furthermore, we prove a general strong law of large numbers for graph-valued random elements.