A Mathematical Analysis of Structural Effects

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The concept of structural effect was introduced to the sociologists by P.M.Blau. He tried to explicate the effects of attributes of social collectivities on individual orientations and conducts. But his discussions were made in natural, non-mathematical languages.In this study, we make an attempt to express Blau's basic idea as a mathematical model. Our major tool is the mathematical theory of absorbing Markov chain. We suggest a concept of mean number of transition before absorption. The interaction processes in social collectivities called structural effects could be explicitly depicted by Absorbing Markov chain. We can expect that this new characteristic value derived from fundamental matrix is a cornerstone for a mathematical analysis of structural effects.