X-Rotary (9): Two-mode networks of meeting attendance

As announced in the introductory post, the first step in our analysis of Rotary networking consists in designing three bimodal networks, one for each term (Petit, Fitch, Harkson). In analyzing two-mode data, we typically make the assumption that attending the same event is either an indicator of an interaction between the attendees or a potential opportunity for one to develop (Borgatti, 2013: 246). In our two-mode networks, nodes refer to either persons or events. Edges represent the roles performed by participants during events (chair, speaker, guest, organizer, etc.). Nodes attributes specify the type of events (regular meeting, closed meeting, outing and other special events) and persons’ status (members, non-members, officers, directors), gender and nationality (Western, Chinese, Japanese, other). For members only, we also specified the classification (business sector) to which they belonged, their affiliation (the organization they represented), their social-professional position (in Fitch and Harkson networks only) and the Rotary committees on which they served (Harkson’s network only). The following graphs (built with Cytoscape) visualize the three networks, one for each time period [Fig. 3a, 3b, 3c]. Square nodes (on the left) represent events, circle nodes (on the right) represent persons. The size and color of nodes are proportionate to their degree centrality. Interactive versions of these networks are available on CytNetShare : Petit, Fitch, and Harkson.

Global description

The following table compares the global measures for each network.

Petit Fitch Harkson
Nodes 104 139 97
Edges 113 153 83
Connected components 14 9 27
Density 0.019 0.016 0.015
Centralization 0.169 0.153 0.091

For a large part, these global measures reflect the uneven quantity and quality of information available in newspapers. Fitch’s term is by far the best-documented period. In the early years (Petit’s term), either we have fewer information, fewer persons were involved or fewer events were organized. The principle of regular weekly meetings was not perfectly established yet. The Rotary was still in the process of settling club rules and members’ roles. The most recent network (Harkson) shows a less cohesive structure, mainly because it is built on more scattered data (27 connected components, compared to 9 in Fitch’s and 14 in Petit’s network). The three networks show a relatively low density – lower than what we could expect in a highly selective club like the Rotary. This is mainly due to the significant participation of outside visitors in club meetings. The density decreases over time. In Fitch’s network, this reflects the highest number of outside visitors, whereas in Harkson’s network, it reflects the growing scarcity of information. Yet overall, there is no a significant change in network density. The structure of the Rotary is rather stable over time. Network centralization also decreases over time, reflecting the declining position of the president at the end of the period. As President Harkson was on leave during most of his term, he is barely mentioned in newspaper reports. As a rule, the vice-president (Wolfe) served as the interim president, but he was far less central than previous presidents (especially Fitch, as we shall elaborate in the next essay).

Degree distribution

In this section, we use node degree centrality to measure the relative importance of events and persons based on their position in the networks. Nodes with high degree correspond to either persons who participated in many events, or to events that gathered many participants (or those on which we have more information). We assume a correlation between degree centrality, on the one hand, and persons’ status or type of events, on the other hand. We hypothesize that key members (president, vice-president, directors and other officers) show a high degree centrality, whereas ordinary members, occasional guests and outside visitors have a lower degree centrality. As for events, we hypothesize that regular meetings have a lower degree centrality than special events. The three networks show a long-tail degree distribution. The following charts compare the degree distribution in the three networks [Fig. 4a, b, c]. The table helps distinguish between events and persons.

Petit Fitch Harkson
Events max degree 24 21 20
Events min degree 1 1 1
Persons max degree 11 23 4
Persons min degree 1 1 1

In Petit’s network, degree distribution ranges from 1 to 24. Highest degrees (24) are associated to special events (farewell party 24, founding meeting 10), i.e. large events involving a lot of participants or events on which newspaper reports provide detailed information.

  • Event-node degree. There is no direct correlation between the type of meeting and degree centrality. This mainly reflects variations in the quantity and quality of information available on each event. Organizing meetings, however, tend to gather more participants (or are better documented than regular meetings). One particular special event (farewell party 24) also attracted more participants than the average.
  • Person-node degree. Only one person has a degree greater than 10 (Petit, degree = 11), which reflects his position as president of the club. 7 persons have a degree between 3 and 4. All are Rotarians, Westerners and men. All non-members, Chinese and women have a degree below 3. There is a “naturally” strong correlation between high degree (active participation in club activities), status (members are more active than non-members), nationality (Westerners are more active than Chinese), gender (men are more active than women). Rotarians with low degree (1) are charter members (who appear only once during the founding meeting) or honorary members (American consul). Officers (secretary, treasurer, and above all, the president) and directors show higher degree than ordinary members (over 3).

4a. Degree distribution in Petit’s two-mode network


In Fitch’s network, the degree distribution is very similar to Petit’s. It ranges from 1 to 23, which suggests stability over time. This global distribution, however, hides major changes in the allocation between events and persons, and a more hierarchical distribution among persons.

  • Persons’ degree. The highest degree is associated to the president (Fitch) (23), which reflects the higher centralization around this prominent figure. The second most influential person shows a degree of 5 only (Honorary secretary Harris and US trade commissioner Williams – a non-member but prominent personality in Shanghai who frequently attended Rotary’s meetings). One person has a degree of 4 (non-member U.S. Commercial Attache Arnold, who shows a similar profile as Williams). Only two members has a degree of 3. The remaining individuals show a degree of 2 or 1. As in Petit’s network, persons with highest degrees (over 3) are usually Westerners and men. On the opposite, lowest degrees (1) are often associated to non-members, women and non-Westerners (Chinese or Japanese). But there are exceptions to this general rule: 23 Rotarians show a degree of 1. Most of them are ordinary members (except for honorary members and directors). Other exceptional cases include a Chinese non-member (Dr. Wu) with a degree of 2 (as a guest invited to attend two different events), a Chinese woman with a degree of 2 (Mrs. Kwok, married to a Rotarian, who served as an entertainer in two events), a Western woman invited as a speaker and organizer (an exceptional situation for a woman, given that women were usually confined to entertaining male Rotarians).
  • Events degree. There is no clear correlation between event degree and type of event. Events with high or medium degrees (from 5 to 21) may be either special or regular meetings. Paradoxically, the highest degree event (21) is a regular meeting. This reflects the fact that regular meetings were better documented in the local press during this period. Conversely, newspapers could not list all participants in large special events.

4b. Degree distribution in Fitch’s two-mode network


In Harkson’s network, degree distribution ranges from 1 to 20. This apparently stable distribution again hides a major change in network structure. The most striking difference with previous networks is the absence of high-degree node-person (this is obvious if we use the “group-by-attribute layout » in Cytoscape). 4 is the highest degree associated to a node-person. This suggests the declining prominence of the president and the growing paucity of information on participants in general. In fact, during this period, newspapers merely mentioned the dates of meetings and the main speaker’s name, and provided few information on other attendees. This is a major limitation in this longitudinal study.

  • Event degree. Highest degrees refer to most important events (5 to 20). All are special events. Low degree points to regular meetings or other events (charity, war effort, inauguration of children’s hospital). For the first time, there is a strong correlation between degree centrality and the type of event. This mostly reflects the fact that special events are better documented in newspapers than ordinary meetings. This suggests that the practice of regular meetings is now a well-established rule and does not need to be reported in detail. But this may also reflect that in wartime, newspapers were more interested in reporting important – international, war-related – events rather than mundane events, except when such events were connected to war effort (fundraising campaigns in aid of war refugees).
  • Persons degree. Degree distribution is more evenly distributed between persons (ranging from 1 to 4). The persons who show high degrees (2 to 4) are all men, Rotarians and Westerners (except for 5 Chinese with a degree of 2). Those with the highest degree (4) are officers (president and vice-president). Fifteen Rotarians display the lowest degree (1), most of them being Chinese or non-American.

What types of role connect the most important persons and events (degree > 10)? In Petit’s network, chair and organizer serve as the most frequent links. In Fitch’s network, this falls to a single role – chair – which is directly related to the president’s pre-eminence. Second-rank events and persons (degree < 10) are connected by guests and speakers.  In Harkson’s network, largest events are connected by organizers and committee members. Events and persons with lower degrees are connected by a variety of roles.  We will explore patterns of roles connections more fully in the last essay (12).

To conclude this two-mode analysis of meeting attendance, we observe that in the long run, person-nodes with high degrees are usually – but not always – key members (officers, especially the president, or directors). Fitch’s personal character – his ubiquity and propensity to coordinate all actions in meetings – may account for the exceptional centrality of the President during his term. None of his predecessors (Petit) or successors (Harkson) can compare to his prestige. Symmetrically, event-nodes with high degrees are often – but not always – special events. Beyond a certain point, event size has a regressive effect on data availability.

In such bimodal analysis, other measures and methods (betweenness, clustering) would not make sense or would be difficult to conduct. We are limited in terms of the analytical tools we can use in two-mode networks. In order to complement this preliminary exploration of attendance, the next essays will offer a dual-projection approach. We will project the initial two-mode networks into two one-mode networks of persons-persons joined by events (co-attendance) and events-events joined by persons (multiple attendance), using the “tnet” R package (project_tm function, Opsahl 2008). We alternatively used and compared two different methods of projection. The “sum” method gives the actual pattern of co-attendance (actual number of co-attended events), while Newman’s method takes the relative importance of events into account, by discounting the largest events (that are the most likely to be attended) and most prominent persons (who are the most likely to attend events). In the following essays, we successively examine networks of co-attendance (10) and of multiple attendance (11).


Borgatti, Stephen P, Martin G Everett, and J. C Johnson. Analyzing Social Networks. Los Angeles, Calif.: Sage, 2013 (chap.13).

Opsahl, Tore. “Two-mode networks.” Tore Opsahl (blog), June 21, 2011. https://toreopsahl.com/tnet/two-mode-networks/ [Last accessed August 29, 2019]


Cécile Armand

Ancienne élève de l'Ecole Normale Supérieure (ENS) de Lyon (2006), agrégée d'histoire (2009), docteure en histoire (2017), postdoctorante à Stanford University (2017-8) puis Aix-Marseille Université dans le cadre du projet ERC “Elites, Networks and Power in modern China” (2018-). Ma thèse soutenue à l’ENS Lyon en juin 2017 proposait une histoire spatiale de la publicité à Shanghai (1905-1949). Mes recherches actuelles portent sur l’émergence des experts, “l’influence” américaine, la naissance de la presse et d’une “opinion publique” en Chine moderne. Dans une démarche d’histoire sociale, mes centres d'intérêt englobent aussi l'histoire spatiale, les outils et méthodes numériques et l'épistémologie des sciences sociales en général.

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Cécile Armand

Ancienne élève de l'Ecole Normale Supérieure (ENS) de Lyon (2006), agrégée d'histoire (2009), docteure en histoire (2017), postdoctorante à Stanford University (2017-8) puis Aix-Marseille Université dans le cadre du projet ERC “Elites, Networks and Power in modern China” (2018-). Ma thèse soutenue à l’ENS Lyon en juin 2017 proposait une histoire spatiale de la publicité à Shanghai (1905-1949). Mes recherches actuelles portent sur l’émergence des experts, “l’influence” américaine, la naissance de la presse et d’une “opinion publique” en Chine moderne. Dans une démarche d’histoire sociale, mes centres d'intérêt englobent aussi l'histoire spatiale, les outils et méthodes numériques et l'épistémologie des sciences sociales en général.

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