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This is the last essay in our series devoted to meeting attendance at the Shanghai Rotary Club. In this post, we propose to analyze the combinations of roles that participants performed during meetings. The following networks result from the projection of the initial two-mode networks of persons-events joined by roles.In this ultimate set of networks, nodes represent role-types, whereas edges represent persons holding multiple roles [Fig. 12a, 12b, 12c]. The absence of ties reflects incompatible roles. The weight of ties expresses the most frequent combinations of roles. On the following graphs, circle nodes refer to roles (behaviors performed during events), while square nodes refer to posts (defined as more stable than roles). To build these networks, I relied on a consistent system of coding that allows for comparisons from one network (period) to the other, helping to identify structural patterns and to trace changes over time. Interactive versions of these graphs are available on CytNetShare (Petit, Fitch, Harkson).[gallery columns="1" size="full" ids="4121,4123,4125"][gallery size="full" ids="4122,4124,4126"]What are the most frequent role associations? Which roles are incompatible? How did behavioral patterns during meetings change over time?The following table [H] compares the global measures in the three networks. The following charts visualize the distribution of tie weights in each network (sum only) [Fig.13a, 13b, 13c].PetitFitchHarksonNodes (roles)171012Edges (role holders)421118Min edge weight111Max edge weight448Table H. Global measures in Petit’s, Fitch’s and Harkson’s one-mode networks of multiple rolesMultiple role-holding during Petit's termIn Petit’s network, tie weight ranges from 1 to 4, which means that up to 4 persons can perform a given role combination. Organizer, chair, speaker and guest are the most frequent roles. They are also the most strongly related to each other, except between chair and speaker (but this may reflect inconsistencies in extracting and classifying roles). Relations between posts and roles indicate that the president (14) and directors (6) are most likely to act as organizers (13). President (14) is the most likely to act as chair (3). Chairs also serve as organizers in many cases (3/13). Organizers (13) are usually speakers (18). Guests as well often act as speakers (8/18), which suggests two different types of speakers: guests and visitors (non-members) invited to give lectures in club meetings, and key members who coordinate meetings (introducing guests, delivering speeches or acting as discussants). Two executive posts (vice-president 20 and treasurer 19) occupy peripheral positions, whereas the president (14), directors (6) and to a lesser extent, the secretary (11), occupy core positions. Other peripheral roles include host (2) and attendee (9), the latter acting as guest or speaker. The following roles appear incompatible: host-chair, attendee-chair (or co-chair), Rotary officer-guest, except for one retiring member (honored at a farewell party), some directors and the secretary, who happened to be guests in outside events (not organized by the Rotary itself). Compatible posts include: president- acting president, director-secretary-retiring member, whereas incompatible posts involve the vice-president, the treasurer and the president (officers could not cumulate executive positions on the same board).[caption id="attachment_4127" align="aligncenter" width="415"] 13a. Tie weight distribution in Petit’s one-mode network of multiple roles[/caption]Multiple role-holding during Fitch's termIn Fitch’s network, tie weight also ranges from 1 to 4. Speaker (18) is the most common role (maximal degree of 7). The most frequent combinations of roles are: speaker-organizer (13) (maximal tie weight of 4), speaker-co-chair (4) (tie weight = 3) and speaker-guest (8) (tie weight = 2). Less frequent combinations involve guest (8) and absentee (1) (which refers to the Prince of Sumatra who declined an invitation) and organizers-representatives (Rotarians acting as mediators in outside events organized by collaborators). We identify two peripheral posts - committee chairman (22) and committee member (5) - whose holders can only act as speakers. Neophytes occupy core positions in this network because four new members were invited to join the club that year. They could only play as guests (weak tie of 1), however, which suggests that they were expected to observe and learn first before becoming more active members. The secretary also occupies a central position, serving as speaker (tie weight = 2) or co-chair (4) (tie weight = 1). Executive posts are incompatible together, except for committee chairmen who were de facto members of their committee, and committee members who could serve as chairmen in other committees. The circular structure of the network reveals that the following roles are incompatible: organizer (13), co-chair (4) and guest (8) (or absentee 1).[caption id="attachment_4128" align="aligncenter" width="415"] 13b. Tie weight distribution in Fitch’s one-mode network of multiple roles[/caption]Multiple role-holding during Harkson's termIn Harkson’s network, tie weight ranges from 1 to 8, which represents the maximal number of multiple role-holders. The network is partitioned into two separate groups of roles. The first group (on the left) includes a single role type (organizer) along with six posts. It is centered on the organizer, which maintains a central position across the entire period. The strongest tie links organizers with committee members (maximal tie weight = 8), whereas the acting president, vice-president, committee chairman and retiring members were less likely to act as organizers (only one occurrence each). The second group (on the right) includes three roles and two posts. Chair (3), representative (15) and speaker (18) are the most central roles, but they are weakly connected to other nodes (tie weight = 1, which means only one holder each). President and past president could equally act as speakers, but the past president was most likely to perform this role (3 cases). Incompatible posts or roles are striking on this network. Chairs, speakers and representatives could not simultaneously serve as organizers. It is surprising, however, that the acting and vice-president never chaired any club meetings. The lack of information probably accounts for these structural holes.[caption id="attachment_4129" align="aligncenter" width="415"] 13c. Tie weight distribution in Harkson’s one-mode network of multiple roles[/caption]In the long-term, Petit’s role-role network appears to be the most complex, hence the most difficult to interpret. Such complexity reflects a period of experimentation during which roles and rules were not clearly fixed. Fitch’s network presents a more simplified structure, in which club roles and posts were now strongly established. Harkson’s network displays a distinct appearance. In contrast with earlier networks, it is partitioned into two disconnected sets of incompatible roles. This suggests that the Shanghai Rotary Club probably passed through a new period of instability. The Sino-Japanese war (1937-1945) may have disrupted the regular functioning of the club, forcing its members to reinvent the rules. Disconnection also reflects the scattered nature of information available in newspapers.