中文摘要：

依据创新能力对集群升级内涵进行了诠释。根据知识和社会关系水平将集群升级转化为由社会网络、显性知识网络和隐性知识网络互动的超网络。运用变分不等式理论和最优化问题的关系，求得网络的洽合流和超网络的均衡状态。探究了集群规模、数量等变动所导致的网络中流和超网络均衡状态的变化，直至最终实现集群升级。最后结合案例分析网络互动的现实意义及今后研究方向。

英文摘要：

In this paper, the industrial cluster upgrading is interpreted based on innovation ability. According to knowledge and social relations level, cluster upgrading is converted into the supernetwork interacted with social, explicit knowledge and tacit knowledge network. By using the relationship between variational inequality theory and optimization problem, the flows hy^＊ ,q^＊ eij ,quj among explicit knowledge network, tacit knowledge network and social network are obtained, and the equilibrium of cluster super-network is also achieved. The change of flows in network and equilibrium of cluster super-network caused by alteration of cluster size, number etc are approached. The cluster upgrade is realized in unceasing variation of equilibrium. Finally, practical significance of interaction among network is illustrated based on case and further research direction is pointed out.