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从图与网络的视角来看,产业系统可看作以产业为顶点、以关联关系为边(弧)形成的产业网络,网络上的许多信息能够揭示产业关联的特征。生成树是图与网络的一类重要子图,必然也能反映产业关联的特征。本文在投入产出模型和产业网络模型的基础上,构建了产业赋权网络模型,并将最大生成树称为产业基础关联树。进一步地,以Kruskal算法为基础设计了确定产业基础关联树的算法。应用实例表明,产业基础关联树以最少的关联关系,最大程度地反映了产业关联结构的特征,并能提取出中心与形心、圈基等重要指标,描述产业网络的结构特征。
From the perspective of network and figure, the industrial system can be regarded as an industrial network formed by taking the industry as the peak and the association as the edge (arc). Many information on the network can reveal the characteristics of the industrial association. Spanning-tree is a kind of important subgraph of graph and network, which can also reflect the characteristics of industry association. Based on the input-output model and the industrial network model, this paper constructs a model of industrial empowerment network, and the maximum spanning tree is called the industry-based association tree. Further, the algorithm of determining the basic tree of industrial relations is designed based on the Kruskal algorithm. The application examples show that the basic tree of industrial relations can reflect the characteristics of the industrial relation structure to the greatest extent with the least correlation, and can extract the important indexes such as center, centroid and circle base to describe the structural characteristics of the industrial network.