Our more alternative notations: A ! B, A ! B, Z Y Z XY Z X Z Z A ! B, and A ! B. Category 5 (CS) gets one more alternative notation, [A !B and A Z Y Y Z Z Z ZB].Finally, category 6 (asocial) gets two more alternative notations, A !B and A B. For any N ! 2, all of the 2N+1 elementary interactions are included in the representative relationships of the six categories and their alternative notations. This results from the building process of the six categories, with the differentiations covering all possible cases. In the example of N = 3, the above statement is illustrated by the comparison of the sixteen elementary interactions of Table 4 with the six categories and their alternative GSK-1605786 cost notations for N = 2 (Table 3), completed by the alternative notations for N = 3 listed above. This concludes the proof of exhaustiveness of the six categories of Table 3 for any number N ! 2 of non-null EPZ-5676 chemical information social actions. With N social actions at hand, richer composite relationships can be represented. Let us translate into our action fluxes representation an example of composite relationship given by Goldman [25] (pp. 344-345). Namely, “two friends may share tapes and records freely with each other (CS), work on a task at which one is an expert and imperiously directs the other (AR), divide equally the cost of gas on a trip (EM), and transfer a bicycle from one to the other S2 S4 S5 S6 S1 S for a market-value price (MP).” This gives [A ! B, A 1 B, A ! B, A ! B, A ! B, A ! B].S2 S4 S6 SHere the relationship was known and we wrote it in terms of action fluxes. The next step is to find out how to identify a relationship when the action fluxes are given. We touch on how to achieve this in the discussion.Discussion Analyzing data setsOur representation in action fluxes provides a tool to identify types of dyadic relationships occurring within potentially large data sets of social interactions. Both collective and dyadic interactions may occur in real social contexts, but our approach applies specifically to the latter. Large data sets can result from any type of online social network or massively multiplayer online role-playing games (MMORPG), for instance. MMORPGs bring hundreds of thousands of players together to cooperate and compete by forming alliances, trading, fighting, and so on, all the while recording every single action and communication of the players. They are used in quantitative social science, for example by Thurner in the context of the game Pardus [26?8]. Ethnological and anthropological studies can provide rich reports of social interactions occurring in non-artificial settings that could be coded and interpreted with the aid of our categorization. Data sets of dyadic interactions can also be generated by computer simulations such as agent-based models (ABMs) to test specific questions. We offer the sketch of a method to analyze a potentially large data set of dyadic social interactions expressed as action fluxes (“A does X to B”, etc.). Given a data set involving a number of individuals, one needs to consider separately each pair of individuals. For each pair, one shall examine each social action and test into which category of action fluxes it falls, possibly jointly with another social action (in the case of MP and AR). In its second column, Table 5 specifies the patterns of fluxes expected to be observed in each category. Let us stress the following points: ?The patterns of observed fluxes given in Table 5 are not meant as definitions of the.Our more alternative notations: A ! B, A ! B, Z Y Z XY Z X Z Z A ! B, and A ! B. Category 5 (CS) gets one more alternative notation, [A !B and A Z Y Y Z Z Z ZB].Finally, category 6 (asocial) gets two more alternative notations, A !B and A B. For any N ! 2, all of the 2N+1 elementary interactions are included in the representative relationships of the six categories and their alternative notations. This results from the building process of the six categories, with the differentiations covering all possible cases. In the example of N = 3, the above statement is illustrated by the comparison of the sixteen elementary interactions of Table 4 with the six categories and their alternative notations for N = 2 (Table 3), completed by the alternative notations for N = 3 listed above. This concludes the proof of exhaustiveness of the six categories of Table 3 for any number N ! 2 of non-null social actions. With N social actions at hand, richer composite relationships can be represented. Let us translate into our action fluxes representation an example of composite relationship given by Goldman [25] (pp. 344-345). Namely, “two friends may share tapes and records freely with each other (CS), work on a task at which one is an expert and imperiously directs the other (AR), divide equally the cost of gas on a trip (EM), and transfer a bicycle from one to the other S2 S4 S5 S6 S1 S for a market-value price (MP).” This gives [A ! B, A 1 B, A ! B, A ! B, A ! B, A ! B].S2 S4 S6 SHere the relationship was known and we wrote it in terms of action fluxes. The next step is to find out how to identify a relationship when the action fluxes are given. We touch on how to achieve this in the discussion.Discussion Analyzing data setsOur representation in action fluxes provides a tool to identify types of dyadic relationships occurring within potentially large data sets of social interactions. Both collective and dyadic interactions may occur in real social contexts, but our approach applies specifically to the latter. Large data sets can result from any type of online social network or massively multiplayer online role-playing games (MMORPG), for instance. MMORPGs bring hundreds of thousands of players together to cooperate and compete by forming alliances, trading, fighting, and so on, all the while recording every single action and communication of the players. They are used in quantitative social science, for example by Thurner in the context of the game Pardus [26?8]. Ethnological and anthropological studies can provide rich reports of social interactions occurring in non-artificial settings that could be coded and interpreted with the aid of our categorization. Data sets of dyadic interactions can also be generated by computer simulations such as agent-based models (ABMs) to test specific questions. We offer the sketch of a method to analyze a potentially large data set of dyadic social interactions expressed as action fluxes (“A does X to B”, etc.). Given a data set involving a number of individuals, one needs to consider separately each pair of individuals. For each pair, one shall examine each social action and test into which category of action fluxes it falls, possibly jointly with another social action (in the case of MP and AR). In its second column, Table 5 specifies the patterns of fluxes expected to be observed in each category. Let us stress the following points: ?The patterns of observed fluxes given in Table 5 are not meant as definitions of the.