7. Let $x_{i} \in \mathbf{R}, x_{i} \geqslant 0(i=1,2,3,4,5), \sum_{i=1}^{5} x_{i}=1$, then $\max \left\{x_{1}+x_{2}, x_{2}+x_{3}, x_{3}+x_{4}, x_{4}\right.$ $\left.+x_{5}\right\}$ the minimum value equals $\qquad$ .
7. $\frac{1}{3}$ Detailed Explanation: $\max \left\{x_{1}+x_{2}, x_{2}+x_{3}, x_{3}+x_{4}, x_{4}+x_{5}\right\} \geqslant \max \left\{x_{1}+x_{2}, x_{1}+x_{4}, x_{1}+x_{5}\right\} \geqslant$ $\frac{1}{3}\left(\sum_{i=1}^{5} x_{i}+x_{4}\right) \geqslant \frac{1}{3}$,
If $x_{1}=x_{3}=x_{5}=\frac{1}{3}, x_{2}=x_{4}=0$, then $\max \left\{x_{1}+x_{2}, x_{2}+x_{3}, x_{3}+x_{4}, x_{4}+x_{5}\right\}=\frac{1}{3}$.