On Web’s contact structure

Abstract

The explosive growth of Web and social networks has revealed the need to (re-)analyze the connection structure of the underlying graphs. Kleinberg et al. in 1999 has defined Web-Graph as the graph induced by the (directed) hyperlinks between the (static) Web pages. Since then, the Web-graph model has been the basis for representing the Web connection structure. In the early ‘90s, many authors conjectured that Web-graph was a scale-free network containing very few huge-degree nodes and many small-degree nodes. Over the years, this conjecture has established itself, although with some minor limitations. Our paper aims to contribute to a deeper understanding of some Web dynamics such as the spreading of information and viruses, the measurement of the real attractiveness of a site or the estimation of a potential power of influence in the propagating of ideas or in the promotion of products. Our working hypothesis was that Web’s spreading dynamics are better analyzable considering the actual contact between nodes in a time interval, since the physical link has some drawbacks: (a) it is quite static, (b) it may remain inactive, (c) many accesses to Web resources are performed online, typing something in an address-bar. We show that Web is still a scale-free network, with three main classes of nodes: very few huge nodes, the hubs, a significant number of intermediate nodes, an huge number of small nodes. Note that mini-hubs meet regularly in the real world: many sites present millions of daily contacts; however, they do not reach the size of an hub, but they are not so small that they can be ignored, like small-degree nodes. We suspect that they may be responsible for the local spread of viruses or information on the Web. To extract the data presented in this paper, we analyzed 19 categories of coherent sites, sub-divided into 309 sub-categories, for a total of 56,450 different sites, and we considered the contacts for the entire month of July 2017, where the average number of unique visitors were 257,022, who visited an average of 4,050,957 pages.

Appendix: Graphics

Fig. 1

Unique visitors: entire corpus (56,450 sites)

Fig. 2

Pageviews: entire corpus (56,450 sites)

Fig. 3

Unique visitors: 9248 sites with rank $\le 100,000$

Fig. 4

Pageviews: 9248 sites with rank $\le 100,000$

Fig. 5

Unique visitors: first 1000 sites by rank

Fig. 6

Pageviews: first 1000 sites by rank

Fig. 7

Pageviews: 9248—log sites with rank $\le 100,000$

Fig. 8

Pageviews: 54,450—log sites

Fig. 9

Pageviews: 9248—$log^2$ sites with rank $\le 100,000$

Fig. 10

Pageviews: 54,450—$log^2$ sites

Fig. 11

Pageviews: 9248—2.5% sites with rank $\le 100,000$

Fig. 12

Pageviews: 54,450—2.5% sites

Fig. 13

Pageviews: 9248—5% sites with rank $\le 100,000$

Fig. 14

Pageviews: 54,450—5% sites

Fig. 15

Pageviews: 9248—10% sites with rank $\le 100,000$

Fig. 16

Pageviews: 54,450—10% sites

Fig. 17

Pageviews: 9248—15% sites with rank $\le 100,000$

Fig. 18

Pageviews: 54,450—15% sites

Fig. 19

Pageviews: 9248—25% sites with rank $\le 100,000$

Fig. 20

Pageviews: 54,450—25% sites

Fig. 21

Pageviews: 9248—50% sites with rank $\le 100,000$

Fig. 22

Pageviews: 54,450—50% sites

Fig. 23

Pageviews: first 25% sites with rank $\le 100,000$

Fig. 24

Pageviews: first 25% sites

Fig. 25

Pageviews: second 25% sites with rank $\le 100,000$

Fig. 26

Pageviews: second 25% sites

Fig. 27

Pageviews: third 25% sites with rank $\le 100,000$

Fig. 28

Pageviews: third 25% sites

Fig. 29

Pageviews: last 25% sites with rank $\le 100,000$

Fig. 30

Pageviews: last 25% sites

Fig. 31

Pageviews: 54,450—25% random sites

Fig. 32

Pageviews: 54,450—50% random sites