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Alex, 

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.

It is common in the network literature to find examples of multiple overlapping networks. The same individuals, for example, may be linked by marriage, advice, trust, mutual assistance, or meeting for lunch, etc. But this links do not arise, as they do in teams where individuals are recruited and assigned to play specific roles and, except in playground or pickup games may have little or no choice in who their teammates are. 

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.

John



Sent from my iPad

On 2015/02/08, at 23:11, Alexander Loewi <[log in to unmask]> wrote:

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?

Best,
Alex.

On Sun, Feb 8, 2015 at 1:59 AM, John McCreery <[log in to unmask]> wrote:
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Dear Colleagues,

On the quantitative side of my research on networks formed by project teams, I encounter the following issue. Members of a team have distinct relationships to the project and thus to each other. Thus, for example, in the advertising industry, the simplest dyadic form of a creative team combines a copywriter with an art director. The former is responsible for words, the latter for the visual image. 

Suppose, for example, that we code these relationships as follows: 1=copywriter, 2=art director. In a 2-mode network of projects whose teams take this form

  • We can imagine a network in which every project has a different copywriter, but some art directors are project boundary spanners who work with more than one copywriter.
  • We can imagine a network in which every project has a different art director, but some copywriters are project boundary spanners who work with more than one art director.
  • Our empirical data show that some copywriter+art director pairs always work together and never work with anyone else but that both copywriters and art directors can be boundary spanners creating links between different projects. 

Our question is how to measure the effects of the two relationships on network properties.

The approach that I have adopted is as follows. Using Pajek, 

  1. I gather basic network information, including average degree, line values, and components.
  2. I extract the large component and gather a second set of basic network information about this subnetwork.
  3. Having converted line values into relations, I remove one of the relationships and note changes in large component subnetwork.

Average degree changes—a predictable consequence of there now being fewer lines in the original network.

The relative proportions of line values also change. Using the hypothetical example described above, in which there are only two relationships, whichever remains now accounts for 100% of line values. In more complex real-world examples, I have up to ten relationships and the changing percentages may tell us something interest.

That said, the most dramatic effect of subtracting one of the relationships is on the large component subnetwork, which now becomes several components, a phenomenon I have labeled “the shatter effect.”  Thus, for example, in my real-world networks, removing one relationship may break the large component into 44 components. Removing another relationship may result in 100 or more. My intuition tells me (1) that this has something to do with the number of edges removed from the original large component and (2) that effects may be disproportionate to the number of edges in question.  I note, for example, that a smaller number of edges, more of which were bridges, might have a larger effect than a larger number of edges, fewer of which are bridges. 

Now, however, I find myself approaching the limits of my mathematical competence. I wonder if anyone has tried a similar approach and, if so, if there are standard ways to measure the disproportionate effects sketched above. 

Your comments and advice will be gratefully received.

John

--
John McCreery
The Word Works, Ltd., Yokohama, JAPAN
Tel. +81-45-314-9324
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