1. The World Wine Web: The Structure of the Global Wine Trade
Kym Anderson
Wine Economics Research Centre
University of Adelaide
Joe Francois
World Trade Institute
University of Bern
Doug Nelson
Murphy Institute
Tulane University
Glyn Wittwer
Centre for Policy Studies
Victoria University

2. What we do in this paper Briefly discuss what network analysis does
Briefly review some basic tools of network analysis
Apply these tools to the global wine trade

3. What are networks?
Any collection of objects in which some pairs of these objects are connected by links.
The objects are generically called nodes; and
The links are generically called edges.
In this paper,
The nodes are countries (national economies); and
The edges are annual exports of wine
Thus, the edges are weighted; and
Since we are using exports, our edges are directed
That is, the edge from France to Germans will have a different value than the edge from Germany to France.

4. Analyzing networks: graphs
Graph theory provides a natural language and set of tools for the analysis of networks.
For relatively small networks, pictures do a great job of illustrating the main elements of the network.
Consider the 15 top exporters and 15 top importers of wine.

5. Wine export links among 15 largest exporters

6. Wine import links among 15 largest importers

7. Analyzing networks: graphs
Graph theory provides a natural language and set of tools for the analysis of networks.
For relatively small networks, pictures do a great job of illustrating the main elements of the network.
Consider the 15 top exporters and 15 top importers of wine.
Unfortunately, for large networks this doesn’t work so well.
Consider the entire WWW for

9. Analyzing Networks: Simple Statistics
A number of simple statistics characterize the structure of the network and can be used to analyze the evolution of the network over time.
In particular, we are interested in:
Size of network
Symmetry or asymmetry of network participants
Centralization and density

10. Analyzing Networks: Simple Statistics
Size is easy. We consider
Number of countries
Number of bilateral links between countries
Total trade volume
The WWW has grown dramatically since the mid 1960s.
# of Countries
165
194
199
198
226
228
231
236
# of Links
1946
2527
3081
3218
3264
4269
4945
6664
7807
8191
Total Trade
595825

11. Analyzing Networks: Simple Statistics
Symmetry/Asymmetry of Nodes
A simple approach is to compare the number of links (“degree”) or the size of trade (“weighted degree”) of the largest exporter (outdegree) or importer (indegree) to the mean and median of these measures.
Max out degree
155
175
183
184
198
201
203
205
210
Median out degree 2 1 3 5 9 12
Max weighted out degree
186341
426262
883433
Median weighted out degree 10 14 25 49
101
134
159
213
Mean degree 13 15 16 19 22 29 34 35
Mean weighted degree
3611
6181
11891
20735
26091
36760
51367
65819
109430
133761
Max in degree 60 58 77 78 90 93
140
114
127
Median in degree 11 17 24
Max weighted in degree
141902
182757
355994
817930
Median weighted in degree
168
308
422
588
764
1324
1551
1669
3305
4760

12. Analyzing Networks: Simple Statistics
Degree distribution
Instead of a normal distribution, the degree distributions of many social networks are characterized by a power law.
That is, degree, say k, obeys a power law if the probability of a node having degree k, P(k), is drawn from a distribution
𝑃 𝑘 ∝ 𝑘 −𝛾 ,
γ is a constant parameter of the distribution called the scaling parameter.
This parameter typically lies in the range 2 < γ < 3.
Such a distribution is called “scale free” (i.e. scaling k by a constant, c, simply multiplies the original power law relation by c-γ).

13. Analyzing Networks: Simple Statistics
Thus, the degree distribution is approximated by a straight line
log 𝑃 𝑘 ~−𝛾 log 𝑘 .
Note that, if this fits the data, the slope of the line is an estimate of the scaling parameter.
That is, there are “fat tails”—i.e. there are more instances of nodes with many links than would be predicted by a normal distribution.
Many social phenomena are characterized by power law distributions
Firm size
City size
Income distributions
We have not tested for this, but will for the final version of the paper.

14. Analyzing Networks: Simple Statistics
Density
The basic statistics suggest that the WWW should have been growing progressively denser.
The standard measure of density is the number of (unweigted) links observed in the data as a proportion of possible links.
The number of possible links is just [n(n – 1)]
Thus, we divide # of links from the first table, by this number.
So density has increased systematically
Density
0.037
0.067
0.078
0.083
0.084
0.096
0.125
0.147
0.148

15. Analyzing Networks: Simple Statistics
Centralization
Centralization is the extent to which a single node dominates all links.
A maximally centralized network is a star (i.e. a network in which each node has degree 1 [or 2 for directed networks], and the center has degree n – 1).
Thus, we calculate the extent to which the WWW deviates from the star network.
That is, we use UCINET to calculate the sum of the differences between the degree of the most central node and all other nodes, as a fraction of the maximum sum of differences

16. Analyzing Networks: Simple Statistics
Out centralization
0.879
0.844
0.85
0.86
0.8
0.75
In centralization
0.296
0.234
0.312
0.315
0.374
0.331
0.316
0.48
0.35
0.39
Not surprisingly, centralization is rather low.
Our centralization declines modestly, but steadily, over this period.
In centralization rises up to the mid-1980s and then stabilizes (with something of an outlier).