The study suggests a model for social network based on a caveman network. The model we propose can fit the following two properties: (1) `small-world property' which has high clustering coefficient, and (2) `scale-free property' which has power law degree distribution. In addition, the model is modified to match the s-metric property. The s-metric property provides a new viewpoint of scale-free network which was proposed last year. In this study, we calculate the s<sub>max</sub> in two ways: one is `simple graph' and another is not limited to simple graph. We believe `simple graph' is reasonable in s<sub>max</sub> property for social network.