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Proxy Networks

Analyzing One Network to Reveal Another
Valdis Krebs
p. 61-70


Réseaux écrans, l'analyse d'un réseau pour en dévoiler un autre: Des données de centres d'achat de livres sur le Web, tel que Amazon, fournissent souvent, pour un livre donné, la liste des autres livres achetés en même temps que le premier. Cette étude utilise cette information du lien entre les achats pour construire des réseaux sociaux de "livres jumelés". Quoique l'orientation politique des acheteurs ne puisse pas être connue, la structure des réseaux de livres jumelés montre qu'il existe deux groupes clairement divisés: un groupe plus grand et plus diffus d'orientation plutôt de gauche, et un autre plus petit et plus serré orienté plutôt à droite. Des types ou des réseaux de lecteurs liés à un auteur donné sont aussi étudiés.

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1The social networks we are embedded in often influence our behavior, our choices, and our opinions. Yet, it is often difficult to map these social networks, to gather network data without intruding on those we wish to understand. Another problem arises when the group we wish to evaluate is large or distributed widely over a large geographic area. Sampling is a common method of gathering research data. Unfortunately, social networks are not easy to sample (Frank, 1981). Although snowball sampling (Goodman, 1961) methods have proven effective in various circumstances.

2A new method of studying behavior in social networks is borrowed from computer networks — the proxy network. A proxy network is a stand-in, or surrogate, for the actual network. The proxy network is easily accessible whereas the network it substitutes for is hidden and difficult to observe. We study a proxy network because it is visible and data is available, and we believe it reveals behavior of the hidden network for which it is an alternate view.

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3The Internet contains the data for many proxy networks. One of the most complete, and updated, proxy networks of human behavior is found at the web sites of major on-line retailers. Book retailers on the web share data about which books were purchased together. Look up any book on and you will see listed the five to six other books that were purchased with the book you have looked up. Amazon has opened up their data base so others can add services to the data Amazon keep on products and purchases.1 Can the book-buying behavior of thousands of consumers reveal interesting patterns and clusters amongst the purchasers?  Is a book network an accurate proxy for the human network that reads the books?

"Buddy Book" Networks

4The network in Figure 1 is a network of books. Two books are linked if they were bought together at a major retailer on the web. I call these "buddy books". A link was drawn if either book of a pair listed the other as a buddy. The data made public by the retailer shows just the "best buddies" — the strongest ties. Other patterns may emerge with investigation of weaker ties. Amazon reveals only the top five or six books bought concurrently with a particular book. Seeing dozens of buddy books for each book would reveal some of the weaker ties and no doubt affect the structure of our network.

Figure 1: Netword of Political “Buddy Books”

Figure 1: Netword of Political “Buddy Books”

5The network in Figure 1 was inspired by an on-line conversation I had with several people during the winter holidays of 2002. The book Silent Takeover by Noreen Hertz was often mention in the discussion. Having mapped out book networks previously, I became interested in what network of books would this one be embedded. As I gathered the buddy book data I started to wonder — would the book patterns reveal political patterns?

6Using snowball sampling — following the connections between books — two distinct clusters emerged. There was only one book that spanned both clusters. Lightly-connected books — peripheral nodes with two links or less — were removed.

7The actual political affiliation of each book buyer is not known, not even by the web retailer. Yet, after thousands of data points, this emergent pattern is curious. Although the data was collected uniformly across all shown books, the cluster on the right contains less books. These readers kept selecting the same few books — their clique of books is dense — 39%. Most books have highly overlapping buddy lists. Slander, Bias, and LetFreedomRing are the most popular buddies in this cluster.

8The cluster on the left reveals a broader array of books. This network is less dense — 19%. It even contains two books (LexusandtheOliveTree and ClashofCivilizations), on the periphery of the cluster, that most people would not group with the other books in this cluster. Is this group partially open to other views? Yet, they have their favorites also — Stupid White Men shows up on almost half of the buddy lists.

9If the network of books is a proxy for the network of individuals who read them — what does the network map reveal? At least amongst book readers there appears to be two obvious divisions in political thought. Although academics and political pundits may read books from both clusters, the common reader obviously does not. They choose books with similar opinions again and again.

10It appears that echo chambers have emerged that repeat a consistent message within each cluster. Burt explains that a tightly closed network "amplifies predispositions, creating a structural arthritis in which people cannot learn what they do not already know" (Burt, 2001). With no direct bridges between the clusters, these divisions are unlikely to change any time soon.

11One of the cardinal rules of human networks is "Birds of a feather flock together". Friends of friends become friends, and coworkers of coworkers become colleagues. Dense clusters of connections emerge throughout social space. The usual pattern found throughout social structures is dense intra-connectivity within clusters with sparse inter-connectivity between clusters.

12In a previous effort at mapping the network around a single book, I began to wonder:

  • How do these listed books relate?
    Are they "books of a feather"?
    Or, are they different — complementary?

  • What do these books say about the community buying them?
    Who are these people?
    What are their goals and interests?
    Are these people I should know (obviously our interests overlap)?

13The key to understanding the dynamics of networks is reading the emergent patterns of connections that surround an individual, or that are present, within and around, a community of interest. I wanted to see the network in which my book of interest was embedded. Seeing those connections would give me insight into the "network neighborhood" surrounding this book and hopefully help me make a smarter purchase.

14I decided to trace the network out one and two steps from the focus book. This is a common procedure in social network analysis when studying ego networks (Wasserman and Faust, 1994). An ego network allows us to see who was in one's network neighborhood, how they are interconnected, and how this structure may influence ego.

15To continue my exploration, I had to choose a book as my focal point, or ego. I chose Tom Petzinger's The New Pioneers. After all, that book was the reason I had originally visited — before I got sidetracked. As I collected the data, I started wondering again:

  • What other topics are Tom's readers interested in?

  • Will Tom's book end up in the center of one large, massively interconnected cluster — a single community of interest?

  • Or, will it end up linking together otherwise disconnected clusters — diverse communities of interest?

16Figure 2 is the network surrounding The New Pioneers. Each node represents a book. A heavy line links books that were purchased together. The buying pattern of the books has self-organized into emergent clusters that I have named after the content of each cluster. It is obvious that Tom's book does span a diversity of interests!

Figure 2: The network surrounding The New Pioneers

Figure 2: The network surrounding The New Pioneers

17Next we examine the network measures (Wasserman and Faust, 1994) of each node/book, to see which nodes are well positioned in the web of connections. The most common measure in social networks is network centrality (Freeman, 1979). To assess "positional advantage", we measure each node's network centrality. We have two parts of the network: 1) the Complexity cluster, and 2) the other three interconnected clusters forming a large network component. The highest scoring nodes in the Complexity cluster are Open Boundaries and Complexity Advantage — they received identical scores. The scores in the large network component, in declining order, are as follows

  • 1. (tie) Management Challenges in the 21st Century

  • 2. (tie) Business @ the Speed of Thought

  • 3. Dance of Change

  • 4. Innovator's Dilemma

  • 5. Information Rules

  • 6. New Rules for the New Economy

  • 7.

18The top two books received the highest scores because they are instrumental in connecting/bridging the three clusters (Internet Economy, Old School, New School). Without these bridging connections, there would be more holes in the network such as those that surround the currently isolated Complexity cluster. Notice that more connections do not necessarily translate to network benefits — Information Rules has the most connections but not the highest network centrality score. In networks, it is not the number of connections one has, but to where the connections lead that creates advantage (Burt, 1992). In networks, the golden rule is the same as in Real Estate — location, location, location. In real estate, it is physical location — geography. In networks, it is virtual location — determined by the pattern of connections surrounding a node.

Structural Equivalence among "Buddy Books"

19Another common network measure is structural equivalence (Lorrain and White, 1971). It reveals which nodes play a similar role in a network. Equivalent nodes may be substitutable for one another in the network. As an author, I would not like my book to be substitutable with many other books! As a reader, I would like equivalent choices.

20Another value-added service that Amazon provides is the reader-submitted book reviews. A person considering the purchase of a particular book may be aided by the many reviews that accumulate over time. Unfortunately, the reviews can be skewed. An author, with a large personal network, can quickly get a dozen or more glowing reviews of his/her latest book posted to Customers who are comparison shopping, based on reader reviews alone, may be mislead.

21Could these community of interest maps work in a similar capacity with other consumer items? If I am not familiar with a product, an author, an artist, a vintage, or a brand, I would like to judge an item by the company it keeps — its network neighborhood.

  • Who points to it?

  • What communities is it a member of?

  • Is it central in the community?

  • Does it bridge communities?

  • Are their equivalent alternatives?

22It appears that, as a customer of Amazon, I could make smarter decisions by viewing the embeddedness of various items they sell in communities of interest — especially if I did not have much experience with the items I am considering purchasing.

23What are some network rules-of-thumb we can distill from this analysis?

241. If you have read one nonfiction book of a structurally-equivalent pair, you may not be in a rush to read the second (the second book probably covers the same information as the first book). On the other hand, you may wish to read all structurally-equivalent fiction titles (can't get enough of those cyber-thrillers).

252. If you liked books A, B, and C and want to read something similar, find which books are linked to A and B and C. You can only see this in the network, you cannot see this in Amazon's individual lists unless you open three browser windows and compare the lists yourself.

263. If you want to read just one book about topic X, find the book with the highest network centrality in the cluster of topic X books. This follows the Google philosophy and may reveal a book with excellent "word of mouth".

274. If the book you are looking for is not in stock, find which books are structurally equivalent to the book you were searching for. These will provide similar content and are available now.

285. A book author and/or publicist could use the knowledge of existing book networks to position a book where there is a hole in the network.

296. A publisher could view evolving book networks — they may change weekly — to adapt its marketing efforts.


30In addition to book networks, other networks have currently been used as proxies for the social networks they reveal. Links between web sites reveal some of the social structure on the WWW. Co-authorship networks (Newman, 2001; Barabasi et al., 2002) reveal the social network of scientists in various fields of study. Citation networks (Bayer et al., 1990) may reveal the respect/influence network in a scientific field. Again, we see data that are public, and easy to obtain, are used to reveal aspects of networks that are usually private with their data hidden from easy access by researchers.

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Barabasi, A.L., Jeong H., Neda Z., Ravasz E., Schubert A., Vicsek T. (2002). Evolution of the social network of scientific collaborations. Physica A 311, (3-4): 590-614.

Bayer, A.E., Smart, J.C., McLaughlin, G.W. (1990). Mapping intellectual structure of a scientific subfield through author cocitations. Journal of the American Society for Information Science, 41(6): 444-452.

Burt, R.S. (1992). Structural Holes: The Social Structure of Competition, Harvard University Press.

Burt, R.S. (2000). Bandwidth and Echo: Trust, Information, and Gossip in Social Networks. Pre-Print: 1-42.

Frank, O. (1981). A survey of statistical method for graph analysis. In Leinhardt, S. (ed.) Sociological Methodology: 110-155.

Freeman, L.C. (1979). Centrality in Social Networks I. Conceptual Clarification. Social Networks, 1: 215-239.

Krebs, V.E. InFlow 3.01 Social Network Analysis Software.

Lorrain, F., White, H.C. (1971). Structural equivalence of individuals in social networks. Journal of Mathematical Sociology 1: 49-80.

Newman, M.E.J. (2001). The structure of scientific network collaborations. Proceedings of the National Academy of Sciences USA  98: 404 - 409.

Goodman, L.A. (1961). Snowball Sampling. Annals of Mathematical Statistics 32: 148-170.

Wasserman, S., Faust K. (1994). Social Network Analysis: Methods and Applications, Cambridge University Press.

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Table des illustrations

Titre Figure 1: Netword of Political “Buddy Books”
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Titre Figure 2: The network surrounding The New Pioneers
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Référence papier

Valdis Krebs, « Proxy Networks »Bulletin de méthodologie sociologique, 79 | 2003, 61-70.

Référence électronique

Valdis Krebs, « Proxy Networks »Bulletin de méthodologie sociologique [En ligne], 79 | 2003, mis en ligne le 04 juillet 2008, consulté le 25 octobre 2021. URL :

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Valdis Krebs,

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