4. If $a+b+c=1$, and $a, b, c \in \mathbf{R}^{+}$, then the minimum value of $\sqrt{a^{2}+b^{2}}+\sqrt{b^{2}+c^{2}}+\sqrt{c^{2}+a^{2}}$ is $\qquad$ .
\begin{array}{l}\text { 4. } \sqrt{2} \text {. } \\ a^{2}+b^{2} \geqslant \frac{1}{2}(a+b)^{2}, b^{2}+c^{2} \geqslant \frac{1}{2}(b+c)^{2}, c^{2}+a^{2} \geqslant \frac{1}{2}(c+a)^{2} \text {, so } \sqrt{a^{2}+b^{2}}+ \\ \sqrt{b^{2}+c^{2}}+\sqrt{c^{2}+a^{2}} \geqslant \frac{\sqrt{2}}{2}(a+b+b+c+c+a)=\sqrt{2} .\end{array}