Reciprocity, multiplexity, and exchange: Measures

We introduce measures and statistical tests for multiplexity and exchange that are modeled on similar ideas developed for reciprocity quite early in the history of social network research. As properties of a multi-relation network, multiplexity, and exchange have almost as ancient a history as reciprocity, but have not been as intensively investigated from a methodological perspective. Multiplexity refers to the extent to which two ties, for example, advice and friendship, coincide over population; that is, do respondents name the same people as friends as the persons they nominate as individuals from who they seek advice. Exchange refers to the extent to which a tie of one type directed from person i to person j is returned by a tie of another type from j to i. We conceive of the current paper as the first part of a two-part paper, wherein the second part explores specific theoretical models for multiplexity and exchange.