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The following are the replies that I have received in response to my
questions about longitudinal analysis of network data. The original email is
at the end.
Many thanks to all those who have provided advice.
I typically include all actors as I want to observe who comes and goes
if you build one file per time period
you can analyze these in ORA - which has built in procedures for
analyzing and looking at networks over time - see www.casos.cs.cmu.edu
then go to tools and to ORA
I was just reading an article in Science by Gueorgi Kossinets and his
advisor Duncan Watts that did a longitudinal study of a university
(that I only discovered I had a copy of because of reading the
archives here!). Here's the link:
They had continuous data but most of their techniques should still
apply to you. In fact, it occurs to me that you are probably wrong to
just compare the network at T, T+1... because the network is probably
not discrete like that, but instead each past state has a varying
amount of influence on the present.
You'll want to read the 'supporting online material' if you have
access to it; it has the 'methods' section. Some excerpts:
They define a "sampling period" tau to determine which links are
considered ongoing links, and which are considered broken. In their
study they chose Tau=60 days which they figured out by analyzing the
distribution of communications (95% of responses came within 60 days).
What is your goal in your study? I'm still just learning SNA but I
keep hitting up against that the appropriate technique really really
really depends on the data
The obvious place to start is the work of Tom Snijders. Google for his home
page. An impressive list of papers on the topic most of them available on
line. His article in the book by Carrington, Scott and Wassermann is also
To examine networks through time (ie network evolution) there are a few
routines that are obvious in exploring the data. Of course it depends on
what your hypotheses are to determine which is most appropriate.
You can do a sampled pair t-test to see if the difference in the networks at
different time points are statistically significant.
Compare densiti.e.s, or correlate the elementary network statistics for
different nodes through time (centrality etc).
You can run simulations through SIENA (part of the stocnet software
platform) testing a number of hypotheses on reciprocity etc
You can examine the network by importing it in netdraw and visually compare
at different time points.
Hope that was useful.
Dr Dimitris C Christopoulos
Department of Politics
Bristol BS16 1QY
I send my reply to you personally, assuming that (like is usual in
SOCNET) you will send a compilation of the answers to the SOCNET list.
If you wish to make a statistical model of the dynamics of the network,
then you could use the methods of
Snijders, Tom A.B., The statistical evaluation of social network dynamics.
Pp. 361-395 in Sociological Methodology - 2001, edited by M.E. Sobel and
M.P. Becker. Boston and London: Basil Blackwell.
Snijders, Tom A.B. (2005). Models for Longitudinal Network Data.
Chapter 11 in P. Carrington, J. Scott, & S. Wasserman (Eds.), Models and
methods in social network analysis. New York: Cambridge University Press.
The fact that actors may have left or entered the network is discussed
for these types of models in
Huisman, Mark, and Snijders, Tom A.B., (2003). Statistical analysis of
longitudinal network data with changing composition.
Sociological Methods & Research, 32, 253-287.
The methods are implemented in the SIENA program, see
One simple way woudl be use QAP or MRQAP if you have control variables. The
correlation between the two matrices would give you a measure to which the
have changed over time.
You may find it useful to look into entropy statistics. I did a paper in
1991 entitled The Static and Dynamic Analysis of Network Data Using
Information Theory, Social Networks 13 (1991) 301-45. You can find it at my
website at http://www.leydesdorff.net/list.htm .
With best wishes,
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> I am trying to solve the following problem: I have relationship data
> collected at various points in time regarding the participation of
> members in a discussion group. Data were accumulated periodically, so the
> network at time T+1 consists of the mapping of all discussions that have
> occurred in the period between T and T+1. The data are in the form of
> adjacency matrices. I need to compare the networks that existed at
> time periods.
> What are some of the ways to compare the network structure at T with that
> T+1? I am thinking of calculating individual-level statistics such as
> various types of centrality (degree, closeness etc.) for each actor in the
> network at both T and T+1 and see how the statistics have changed. Is
> approach correct? In addition, I will also compare network-level
> statistics such as centralization of the network at different time
> Should I include all the actors in both matrices, even though some of them
> have not contributed to the discussion at either T or T+1? Or, should the
> adjacency matrices for specific times include only those actors that have
> contributed? What the relative merits and demerits of these two types of
> representations? What are some good references to which I may refer?
> I am using the SNA library in R for my computations.
> Any advice is much appreciated.
> Thank you.
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