The Bow-Tie Structure in eBay Network
Link: https://pdfs.semanticscholar.org/be3b/e42db8e6b24fdb5d3630508800be7417f04d.pdf
In class we’ve discussed the complex structure of the World Web Web, which we name as the bow-tie structure. It’s natural to take a further step and discuss the universality of the specific structure — whether it exists in other networks and the difference between them. The bow-tie structure is actually observed in many different network systems —for example, the links between different topics on Wikipedia form a bow-tie-like structure. And some Q&A sites as Java Forum also have a similar structure. So, the link above takes eBay, an online market site, as an instance and uses the bow-tie model to analyze the complex network of it. The paper not only discusses the application of bow-tie structure under a specific scenario, but also analyzes the reasons why the model shows a different result. We can see how bow-tie structure reveals deeper features of a network in this paper.
The eBay network is modeled as a weighted directed graph. The paper makes the following assumptions:
- Each vertex denotes an eBay user.
- An edge is created when a user buys something from another user. The direction denotes the seller-buyer relation.
- The number of transactions between the same seller and buyer determines the edge weight.
Note that the weight of the link is not taken into consideration when we are talking about the bow-tie structure.
Under the above assumptions, the paper draws the network of eBay under the bow-tie model. The result is as Figure 1 shows.
Figure 1: The eBay network has an unsymmetrical bow-tie structure
The fraction indicates the ratio of each part. Compared with the structure of WWW, we have the following findings.
- The structure of eBay is unsymmetrical — the OUT part is much larger than the IN part. To understand this feature, we need to have a rough analysis of what each part denotes. Based on the assumptions above, the OUT group are actually those “pure buyers” — who only buy things from others and seldom sell anything. On the contrary, the IN group are those “pure sellers”. So, a high OUT-IN ratio indicates a large group of casual buyers or a few dominant sellers. And this conforms what the data shows — based on the data the paper uses, 82.5% of the users only buy, and 5.76% of the users only sell.
- The SCC of eBay network is much smaller than that of WWW. This feature has something to do with the nature of different networks. As the paper points out, WWW and Wikipedia are both information networks, which reflect the underlying organization of knowledge and concepts. That is, different knowledge tends to link with each other and forms a central part. The eBay network, as well as the Java Forum, consists of social interactions instead. The destinations of the interactions are much more than the sources of the interactions.
- The tendrils are much larger than those in WWW. This phenomenon can also be explained by the nature of eBay network. As social links don’t tend to be connected, it’s more possible to generate tendrils instead of connecting to the SCC.
The paper also discusses the bow-tie structure under different categories. They find that there’re two different types. One is a collector network who has a large SCC as users are willing to exchange their collections like stamps. The other is a retail network which is quite similar to the overall structure — less sellers with large amount of casual buyers. The paper also includes analysis about local structures using triad significance profiles. It’s quite interesting to learn the application of bow-tie structure in different networks. Further work may concentrate on the deep meaning of different parts of the model and analyzing the dynamic changing of the structure.