Lecture 8: Similarities and Differences in Networks

Lecture Overview

Welcome to the eighth lecture for the undergraduate social networks course at the University of Maine at Augusta, in which we continue our discussion of 2-mode networks. There are a number of ways in which 2-mode matrices can be converted to 1-mode matrices not as a way of discussing group affiliation, but rather as a way of comparing node characteristics and experiences. 2-mode matrices can also be used to describe closeness or distance, similarity or difference, and cooperation in activity or inactivity. If we are interested in explaining social distance or why people join together to seek common outcomes, working with 2-mode comparisons can be very handy.

The readings for this week, Wagner et al’s “Organizational Demography and Turnover in Top-Management Groups” and Domhoff’s “Interlocking Directorates in the Corporate Community,” are short but written at a professional level at which meanings are dense and require a great deal of care to understand. You may find it helpful to follow all elements of this week’s lecture before heading to the course syllabus and beginning your readings.

Our lecture subjects this week are:

Course Logistics

One feature I’d like you to notice for this week is… the lack of homework!  Yes, you read that right in the syllabus.  You’ve recently completed an exam, and we’re about to begin a final push to master some new techniques of social network analysis, and of course you should familiarize yourself with the content of your readings and the lecture, but in terms of homework this week I wanted to give you a break to help you get through the difficult “hump time” that the middle of the semester can bring otherwise.  The participation section of this lecture is also suspended for this week to give you a bit more room.  Please take a few moments to breathe at this time of the semester when I know you usually don’t get that chance.

I’d also like to share the good news about how students in general have done on the networks exam.  More than 70% of students who completed the midterm exam got a grade in the B range or the A range.  That’s very well done and you should really be encouraged about what you’ve been able to do, especially considering that some of you reported feeling very nervous at the beginning of the semester.  You see, you can do it!  If you are one of the minority of students who is struggling in this class, please try to let me know as far in advance as possible when you are having trouble with your work.  I’d be glad to provide feedback and help nudge you on the right track, but it helps to have enough time before the due date of an assignment to discuss those problems.


Working with 2-mode Matrices for Social Comparison

In the following video, we consider a number of ways in which 2-mode matrices can be converted to 1-mode matrices as a way of comparing node characteristics. To provide a concrete example of using 2-mode data for comparison, real-life 2-mode information from the Maine State Legislature is included. Why would we want to work with 2-mode information? The explanation of variation in an outcome of importance is one good reason.

In the above video, individual attributes are described in binary terms — that is, they take on a value of either “0” or a “1.” But some attributes move beyond the binary. Consider age, for instance, in the following imaginary world of five people:

The ages of Alice, Ben, Carl, Danielle and Edgar are 45, 20, 62, 17 and 30 respectively

A 1-mode matrix describing the relations between these individuals could describe their difference in years of age:

The Age Differences between Alice, Ben, Carl, Danielle and Edgar

In another comparison that goes beyond binary, consider the following 2-mode matrix of cities in Maine, including information about each city’s location in latitude and longitude:

City Latitude Longitude
Auburn 44.0892 70.2414
Augusta 44.3235 69.7653
Bangor 44.8109 68.7830
Bar Harbor 44.3859 68.2095
Calais 45.1660 67.2424
Fort Kent 47.2549 68.5854
Houlton 46.1221 67.8390
Kittery 43.0897 70.7411
Lewiston 44.0975 70.1924
Portland 43.6651 70.2691
Rockland 44.1096 69.1147

How do these cities relate to one another in terms of location?  BlueMM kindly shares a formula for converting two cities’ latitudes and longitudes into distance in miles:

Distance between City A and City B in miles = ArcCosine(Cosine(Radians(90-Latitude of City A))*Cosine(Radians(90-Latitude of City B))+Sine(Radians(90-Latitude of City A))*Sine(Radians(90-Latitude of City B))*Cosine(Radians(Longitude of City A-Longitude of City B)))*3958.756

Do I expect you to remember or use that long formula?  Absolutely not!  But what I would like you to remember is what formulas like this can find you: a way to describe relations between communities.  In this case, you get a matrix of distances in miles between cities:

Auburn Augusta Bangor Bar Harbor Calais Fort Kent Houlton Kittery Lewiston Portland Rockland
Auburn 0
Augusta 28.608 0
Bangor 87.5246 58.9189 0
Bar Harbor 102.65 76.9789 40.721 0
Calais 165.162 136.798 79.179 71.7993785 0
Fort Kent 232.873 210.359 169.13 199.055537 157.96 0
Houlton 182.888 155.65 101.49 121.30439 72.068 85.89454 0
Kittery 73.4426 98.1963 153.71 154.882827 225.1 306.3127 253.4876 0
Lewiston 2.49927 26.2962 85.212 100.151031 162.74 231.5297 180.9181 74.846 0
Portland 29.3318 51.9297 108.06 113.791511 181.82 261.0919 207.2598 46.287 30.11601 0
Rockland 55.9264 35.4478 51.141 48.6971438 117.47 218.8193 152.3223 107.64 53.47917 65.17326 0


The mathematics used above, whether simple or complicated, is nothing more than a tool like a screwdriver, a wrench or a lathe: it turns raw information into something else, something useful, something that could have real-life meaning for you.  In this case, we get a picture of possible social relationships between cities: if the cities that are closest to one another have more interaction with one another, then we have an idea of who will find marriage partners where, who will make sales where, and possibly even the paths by which epidemics will spread.

Accessing Articles via UMA Libraries

One of this week’s readings is not presented to you in the syllabus as either a direct link or a passage that you could find in one of your textbooks. Instead, it is a reading that can only be accessed by using the password-protected databases of the University of Maine online library system:

Using “the password-protected databases of the University of Maine online library system” might sound complicated and daunting, but I promise that it isn’t. This video was produced for the Spring 2014 version of this course, but the techniques for obtaining one of our readings, demonstrated step by step, still work:

Once you’ve gone through the process once, it’s much easier the second time. Some day when you have an extra moment, I encourage you to poke around in the University library system. It’s amazing how much information is at your fingertips — and available to you for free if you are a registered University student.

Difference and Turnover in the Corporate World

By now, you should have reviewed both videos above (if you haven’t, head back up there and watch!). In the first video of this lecture, I tried to tackle the “why do I need to know this?” question that frequently comes up with network techniques: if you care about any meaningful social outcome, like the passage of laws, then it’s crucially important to be able to find out what kind of social factors (shared race, shared gender, party loyalty, committee service and so on) are most strongly associated with that outcome.

If you’re in business, a shorter answer might be that “it’s all about the money.” Gary Wagner, Jeffrey Pfeffer and Charles O’Reilly’s 1984 article in Administratve Science Quarterly (which you are reading this week) takes an important step forward in predicting instability in corporate management. Turnover in corporate leadership is a costly disruption that, all other things being equal, should be avoided. But how? Wagner et al argue that blaming individual corporate leaders for corporate turnover misses the point:

“What studies in both traditions have tended to overlook is that organizations are fundamentally relational. Thus, to examine the effect of education, age, or length of service [of individual corporate leaders] on an individual’s turnover is to miss the possibility that what may be critical is not an individual’s characteristics in isolation, but rather, the relationship of his or her attributes to others in the organization.”

If birds of a feather flock together, then shoving together birds who aren’t of a feather may produce a noissome, inefficient and ultimately unstable flock. This is the Wagner hypothesis — and to test it Wagner and his colleagues essentially created a two-mode matrix containing information on the age and longevity of corporate managers in a firm, then compared managers to one another to figure out how much difference in age existed within different management groups. The more different managers are from one another in longevity, the more turnover there is in a firm — and the more different managers are in age from the rest of the managers they work with, the less likely they are to stay in a firm. Difference from others in age, not individual age itself, leads to greater turnover and therefore greater cost to a business. What corporate leaders don’t know about their social structure can hurt them. On the flip side, smart business leaders who know why and how to measure the network structure of their organizations can find a clearer path to success.

What about your second reading, G. William Domhoff’s “Interlocking Directorates in the Corporate Community“?  It turns out that this reading is directly is directly relevant to your homework of last week, in which you collected interlocking board directorships for six corporations in the Fortune 500.  Domhoff’s work on network connections among America’s corporate leaders is about a decade old at this point; what’s been going on since then?  We’re going to find out, and you’ve provided some of the necessary detail to make that happen.  Over this week, as I grade the two-mode to one-mode homework you’ve just turned in, I’ll be combining our work into a larger picture of connections not just between six corporations, but between all the corporations that all students in this course have researched.  Stay tuned for the bigger picture in next week’s lecture.

12 thoughts on “Lecture 8: Similarities and Differences in Networks

  1. Pingback: COM/SOC 375: Social Networks at UMA

  2. Another good lecture. definitely starting to see how attributes are related to outcome. For example for the homework, one of my additional attributes was gender and i found that on the appropriations committee was lacking female members comparatively which means that female oriented appropriation bills are less likely to be passed.

    • An interesting result, Cap! Did you find that female oriented appropriation bills are less likely to be passed as a factual pattern, or is this a result that you assume would follow from the fact of a lack of women on the appropriations committee?

  3. Prof. Cook,
    Can we post one excel sheet with tabs at the bottom as you did in the video or would you rather have individual matrices?

    • Thanks for writing, Orion. I suppose that as long as the information is incorporated in a file I can read, it’s equally OK for that file to be an Excel file or a Word file.

  4. Another very interesting lecture and the videos definitely helped to clear up a few things for me. However, as I am currently working on the homework assignment, I am using republican and democratic parties and gender as my two attributes. But as I am looking into one of my committees (of small businesses specifically) all of the members that the website makes available to me are just republican. Is this going to mess up my results? My matrix is going to be somewhat incomplete without democratic members as well. I looked all over the website and they only give me fifteen members in all an they are all republican from what I can see.

  5. I have tried to watch the two videos on this lecture three different times, restarting the computer each time and they seem to be loading but never progress past a certain loading point. Is anyone else having this problem? Is there something other than restarting my computer that might help resolve this problem?

  6. I understood last weeks homework and matrix to a point. By that I mean, I was able to complete it and had a strong idea of what was going on. Now your lectures are not the problem, but I have a question about the last few minutes of it. The formulas you presented are not available on our regular Excel or Node XL correct? Is this something we are going to have to recreate in the future? If so, what program do we use?

    • Virgo,

      Fair question! You’ll notice I didn’t ask you to work this week’s approach out using software, which is exactly because of what you suspect — Excel doesn’t have an easy way to approach the problem. Other software (UCINET and a package called R) can do this, or you can do it yourself by hand. I won’t ask you to try this except with a set of network data small enough for you to manage by hand.

      Prof. Cook

  7. Great lecture. Not to long, but rich with solid information. I do like how you show a new idea, and then show a step by step analysis of what is going on within the problem.


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