Thank you. This kind of feedback is great. The way you can have 10 different kinds in a 2-mode network is that "10 different kinds" refers to relationships, while "2-mode" refers nodes. My empirical case is a bit more complicated, with attributes that partition the nodes in one of the two modes. This is, I expect, a common phenomenon in organizational life but one that has been rarely if ever addressed in the network analysis literature.
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I am writing about the Japanese advertising industry in the period from 1981 to 2006. The projects are ads that made it into the annual published by the Tokyo Copywriters Club following its yearly ad contest. The period in question is interesting in several respects including the economic bubble of the late 1980s and the "lost years" since the bubble crashed in 1991. It is also a period which saw a growing consolidation of the grip of the industry's two largest agencies, Dentsu and Hakuhodo, on what is still today a highly oligopolistic industry. But the analytic question here arises from another phenomenon. These were the years in which TV, having surpassed newspapers in share of total billings in 1975, came to dominate the industry while print media, newspapers and media began what seems to be an irreversible decline. Which brings us to the problem at hand.
TV teams are on average twice the size of print teams (roughly 10 versus 5). Both types of teams have core members. Both types of teams typically include copywriters [relation 1] and creative directors [relation 2]. Print teams will also include art directors [relation 3], while TV teams may, instead include a CM planner [relation 4]. These are typical role combinations in what I call the core team that comes up with the advertising idea. Once the client has bought an idea the core team is expanded to become the production team. In the case of TV, a producer [relation 5], film director [relation 6], and cameraman [relation 7] are essential. In the case of print ads, a designer [relation 8] and a photographer [relation 9] will appear. Other specialists may be involved, an illustrator instead of a photographer, for example. If models are involved, stylists and hair and makeup artists will be added. TV involves sets, lighting, music, recording, video editors and sound engineers. For the moment, these are all simply treated as "Other" [relation 10] in my study.
Where things get hairy is that these relationships are not attributes. It is not uncommon for the same individual to be credited with two or more roles, in the same or separate projects. The same name may appear as copywriter and creative director, for example.
This is the context in which some roles may have greater effects on industry network properties than others do. I began, for example, with the notion that specialists like film directors, cameramen and photographers would be more likely to span institutional boundaries between ads produced by different agencies. Now I am also thinking about creative directors, who have a direct say in who belongs to their teams but are also more likely to be career employees of one of the large agencies instead of freelancers.
More generally speaking, I think that the kinds of problems this data raises can be found wherever there are teams. Those who enjoy sport may think of a favorite game. I think, for example, of baseball. A baseball team requires a pitcher, a catcher, infielders and outfielders. Are some more likely to be traded than others? How does this affect relationships between teams? Is baseball different in this respect from football, in its American football, rugby, Aussie rules, or soccer variants?
Anyway, this is where I am coming from. I am still thinking this through and much remains unclear. Thank you again for the feedback. More questions are welcome.
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Hi, a few things to clarify:
-- I'm not entirely sure what you mean by "relationship" here -- an edge of the form artist-writer/art-art/wr-wr? A "6boundary-spanner"--"boundary-spanner"? I don't see yet how you could have 10 different kinds with only a 2-mode network -- do the real world examples have more modes?
-- You're looking for a metric that describes the degree of "shatter" for each type of relationship -- but want it to be constant for different densities? Or want it to to be conditional on densities?
In general, it sounds like you're looking for a "robustness" measure, and that's the literature I'd start with (with which I'm only anecdotally familiar), but I'm just trying to figure out exactly what kind of a statement you're trying to make. I think lots of basic metrics would be quite expressive. For example, "average number of shards produced per edge removed," for each kind of relationship sounds like it would get at what you're talking about pretty successfully -- the biggest problem I can think of with it is that it might not be comparable across networks of different sizes if the nodes are degree-constrained, but that sounds like a pretty secondary concern too. Would that capture what you're looking for?