X-Rotary (11): One-mode network of multiple attendance
In order to complete our dual projection approach, we now propose to analyze the networks of events-events joined by persons – or networks of multiple attendance at Rotary meetings.
In the following networks, nodes represent events, whereas edges represent persons who participate in multiple events [Fig. 10a, 10b, 10c]. The absence of ties reflects events that have no participants in common. The weight of ties expresses the number of multiple participants (sum method), discounted for persons’ prominence and hyperactivity (Newman’s method). Interactive versions of these networks are available on CyNetShare: Petit, Fitch, Harkson.
The following table [G] compares the global measures in our three sample networks. The charts above compare their tie weight distribution [Fig. 11a, 11b, 11c].
|Edges (shared participants)||40||263||11|
|Min edge weight (sum)||1||1||1|
|Max edge weight (sum)||5||3||2|
|Min edge weight (Newman)||0.143||0.045||0.333|
|Max edge weight (Newman)||3.119||2.045||2.0|
Table G. Global measures in Petit’s, Fitch’s and Harkson’s one-mode networks of multiple attendance
Multiple attendance during Petit’s term
Petit’s events-events network includes 15 nodes (events) and 40 ties (shared participants). Tie weight ranges from 1 to 5, which indicates maximal number of 5 shared participants and represents the highest score in all networks. Events with high degree centrality (i.e. the most likely to share participants) are founding meetings and special events (farewell party, outside dinner). Usually, these events are linked by the strongest ties, which means that they have the highest number of shared participants. Events that are linked by strongest ties (5) are the four founding meetings hold in July 1919 (except for the second one that was more selective and gathered a limited number of founders only), a farewell party (8) (October 1919) and an outside dinner (11) that was not organized by the Rotary itself, but was attended by two Rotarians. Their high scores are hardly surprising because these events gathered a lot of participants. More generally, ties (shared participants) often linked meetings that revolved around similar topics or formed a series of related events (lectures, organization). For example, events 13 and 14 were both devoted to the movie industry and part of the same series of lectures on cinema. More narrowly-focused events are more likely to be isolated from the rest of the network (13/14, 9/12).
Newman’s projections do not make a significant difference, except for stronger ties between events 8-20 (a farewell party and a regular lecture meeting on aviation) and 5-9 (two regular meetings devoted to business and industry-oriented topics). Overall, Newman’s method upgrades a few regular meetings and maintains the core position of founding meetings.
Multiple attendance during Fitch’s term
In Fitch’s network, degree centrality is not an interesting measure since event-nodes are dichotomized into very large (well documented) and very small (poorly documented) meetings. In contrast to Petit’s network, regular meetings have high degrees, whereas special events show the lowest degrees. As we observed earlier, this simply reflects the fact that regular meetings are better documented in the local press (at that time, newspaper accounts systematically listed the names of the most frequent participants but omitted the majority of guests in large gatherings).
Most events have only one participant in common (tie weight = 1). The strongest ties (weight = 3) link events 7-12, 12-19, 19-22, and 33-34. Each pair share three participants. Dyad 19-22 is the only one to be connected by the same topic (series of lectures on the telephone). Other strong ties are associated to high-degree events (large events with many participants). The second most frequent pairs of events are those sharing two participants (tie weight = 2). Some of these pairs have co-participants in common, then forming cliques such as 7, 8, 12, 28 or 1, 7, 8, 12. Usually, these medium-strength ties do not represent similar topics, but translate the fact that large events are more likely to share participants – except for the triad 32-33-5 dealing with international relations and peace, dyad 33-11 dealing with Rotary international, and 33-21 that is loosely connected to universal topics (human race and Rotary International). These examples express Rotary’s interest in global issues and the strong connection between local club lectures and world political concerns in the early 1930s.
Newman’s projections consolidate the central position of topic-related events (33/34, 19/22) and reevaluate the position of peripheral events (23 on Siam, 4 on Poor Russian children). Paradoxically, some events dealing with similar topics are totally disconnected (7 and 4 on Poor Russian), which probably reflects the lack of information on co-participants.
Multiple attendance during Harkson’s term
In Harkson’s network, the maximal number of shared participants (2) is inferior to previous networks. This again reflects the growing scarcity of information in newspapers reports (more than often, they only mention the date and the speaker’s name). This network also shows a more scattered structure. As in previous networks, dyads that have only one participant in common are the most frequent. Four pairs share the same participant (Vice-president Wolfe), then forming a clique. Two dyads have two participants in common (different for each pair). In two cases, links express similar topics (12/28 children outing/Christmas party and 9/18 funerals/religion).
Newman’s projection maintains the clique and the strong connection between 12 and 28, and upgrade the weight of ties between 2-12, 30-23 and 18-9 (disconnected in terms of topics).
In the next post, we propose another way to treat persons as edges by examining more closely the combinations of roles that participants performed during events.