site:{university domain (A)} linkdomain:{university domain (B)}

and to obtain the total number of pages indexed in the university domain (A):

site: {university domain (A)}

     A SQL routine was used to submit the 1 001 000 needed queries to built the link matrix.

     Geographical Map
     We have built a geographical map in order to show the distribution of pages and link flows at the level of countries. To design a geographical map we need a base map which contains the political boundaries of the World. This base map was downloaded from Blue Marble Geographics web site (www.bluemarblegeo.com). Then, we used the Geographical Information System (GIS) software MapViewer 6 to build the final map. This map has two layers: a hutch map which represents the number of web pages by country and a flow map which shows the links between countries. The classification method used in both layers was Jenks’ natural breaks (Jenks, 1963). This method determines the best arrangement of values into classes by iteratively comparing sums of the squared difference between observed values within each class and class means. This method improves the visualization and the interpretation of the results, because it creates more significant differences between classes.

     Network Graph
     A network graph was build with the in-links between the 1 000 university web domains. Several variables have been used in order to add information about the network configuration. Nodes size shows the volume of web pages that each university publishes on the Web, colours represent the nationality of each high education organization and arc size shows the frequency of links between two university domains.
     The software used to visualise the network was Pajek 1.02. We selected a cut-off of minimum 50 links to improve the network visualization. Also we used the Fruchterman-Reingold algorithm to lay out the network because it is the fast for large networks (de Nooy, Mrvar & Batagelj, 2005).
     Several social network indicators were used to describe the network topology and the main characteristics of the nodes:

• K-Core: a sub-network in which each node has at least degree k. K-Cores allow us to detect groups with a strong link density. In free-scale networks, i.e. the Web, the core with the highest degree is the central core of the network, detecting the set of nodes the network rests on (Seidman, 1983).
• Degree: the number of lines connecting a node. This can be normalized (nDegree) by the total number of nodes in the network. In a directed network such as the Web we can count only the incoming links (InDegree) or the outgoing links (OutDegree). In Webometrics, InDegree allows us to detect the visibililty of a web domain (Cothey, 2005; Kretschmer & Kretschmer, 2006).
• Betweenness: the capacity of one node to help connect those nodes that are not directly connected to each other. Its normalization is the percentage over the total number of nodes in the network. From a webometric point of view, this measure allows us to detect hubs or gateways that connect different web networks (Faba-Pérez, Zapico-Alonso, Guerrero-Bote & Moya-Anegón, 2005).

     Results

     Descriptive analysis
     Prior to the link analysis we made a frequency distribution by country of the 1 000 universities.

     Table 1 shows the number of universities by country, listing only the first 15 countries. The United States (US) universities are 36.9% of the entire sample, trailed by the United Kingdom (UK) (6.8%) and Germany (6.6%). This distribution is also observed in the Top 200 of the ranking which suggests that there is a digital divide in favour of US universities. The low performance of emerging countries like Russia (0.6%) and India (0.4%) is also clear.

     Geographical Map

Figure 1. Geographical map of the distribution of pages by country and their link flows

     Figure 1 shows the geographical distribution of web pages by country and the incoming and outgoing links among these countries. Two regions stand out for their large amount of web pages: North America (USA and Canada) and the European Union (EU) zone. The USA is the country with most web pages (50.57%), holding half of the world academic web pages indexed in Yahoo! Search. It is followed by Germany (7.14%) and the UK (4.28%) in the EU. Besides these zones, notice the web development of Japan (2.35%), Australia (2.35%) and China (2.33%) in the East and Brazil (.94%) in South America. Contrarily, two zones have no universities in the sample: Africa (with the exception of South Africa) and the Middle East (with the exception of Israel and Arabia Saudi).
     From the US position, the upper loops show the outgoing links and the lower loops the incoming ones. The most important link flows are between North American countries and EU countries, while in a second ring are links between East Asian and Oceanic countries and the US.

     Network Graph

     The World class network (Figure 2) shows small-world properties because its clustering coefficient (C=527.25) is considerable higher than the same for a random network (C= 35.14) (Watts & Strogatz, 1998). Furthermore, its average path length (l=2.26) is also rather low. Visually, small-world properties can be seen through the traversal links that run across the network, connecting distant clusters (Figure 2). Thein and out degree frequency distributions follow a power law trend (?in= .81; ?out= .73) which allows us to state that this network owns scale-free properties as well (Barabasi, Albert & Jeong, 2000).

Figure 2. Network graph of the World class universities on the Web (N=1 000 arcs= 50 links)

     Figure 2 shows the graph of the 1 000 higher education institutions. First, each university is linked with the universities of its own country. Thus, we can visually detect homogeneous national groups such as Germany (red), the UK (light green) or Japan (orange). However, we can also see that there are countries that do not constitute a compact group such as France (dark blue), Canada (white) and other countries with a small set of universities such as the Netherlands (dark red). This may be due to some countries are included in other larger national sub-networks, indeed Canada is related to the US and the Netherlands with the UK. This describes a cumulative process in which each national sub-network is aggregated to other one like an accreation model.
     The graph also shows linguistic (Thelwall, Tang & Price, 2003) and geographical relationships (Thelwall, 2002). The European countries are located on the right side of the picture, while the left side is mainly taken up by Asian and American ones. It shows, for example, that Spanish universities are between the European and the Latin-American ones, relating linguistic aspect with geographical proximity. In a similar way, Australia is located between the USA and the UK.
     Observe that size is related to link attraction, because the large universities are located in the core of the network. Nevertheless, some countries, specifically Asian ones (China, Japan and Taiwan), have large universities that are far from the core. This may be caused by low development of English pages by these countries (Vaughan & Thelwall, 2004).

Figure 3. Detailed view of the central core of the network

     The main core of the World network was detected with the k-cores method. The central core is 116 nodes with degree 93. This highly connected cluster has 98 American universities. The rest are from Canada (7) and Europe (11). Figure 3 shows in detail this central core, highlighting universities like Harvard, Stanford or Massachusetts Institute of Technology (MIT) which are located in the centre of the graph and attract a huge amount of links from the entire network. Next, the important European universities in the core of the network pull their national networks, as with Cambridge of the British network, Trier of the German one or the Swiss Federal Institute of Technology Zurich (ETHZ) of Switzerland. However, despite the closeness of the Australian universities (purple), there is no presence of Asian, African and Latin-American universities, with the exception of the Israeli ones which are located around the Unites States sub-network.
     We also calculated the in- and out- degree of each university and ranked it. United States universities are the most interconnected in the network. MIT (78.1) and the universities of Berkeley (73.5) and Stanford (73.1) are the web domains most linked in the network (Table 2). Contrarily, the universities that keep the network more connected, making outgoing links, are US as well, particulary the universities of Wisconsin-Madison (47), Stanford (41.8) and Florida (41.2) (Table 3). Notice that both tables only include US universities and the first European universities in the indegree rank are Cambridge in 18th and Leeds in 19th. In the outdegree, the first are ETHZ in 15th and the University of Amsterdam in 22nd.

University	Domain	InDegree	nInDeg
Massachusetts Institute of Technology	mit.edu	781	78.1
University of California, Berkeley	berkeley.edu	735	73.5
Stanford University	stanford.edu	731	73.1
University of Illinois at Urbana-Champaign	uiuc.edu	666	66.6
Harvard University	harvard.edu	634	63.4
University of Michigan	umich.edu	634	63.4
University of Wisconsin-Madison	wisc.edu	629	62.9
University of Texas at Austin	utexas.edu	589	58.9
Cornell University	cornell.edu	557	55.7
University of Washington	washington.edu	555	55.5

Table 2. First 10 universities by their InDegree

University	Domain	OutDegree	nOutDegree
University of Wisconsin-Madison	wisc.edu	470	47
Stanford University	stanford.edu	418	41.8
University of Florida	ufl.edu	412	41.2
University of California, Berkeley	berkeley.edu	411	41.1
University of Washington	washington.edu	390	39
Massachusetts Institute of Technology	mit.edu	378	37.8
University of Illinois at Urbana-Champaign	uiuc.edu	369	36.9
Carnegie Mellon University	cmu.edu	365	36.5
University of Pennsylvania	upenn.edu	360	36
Harvard University	harvard.edu	356	35.6

Table 3. First 10 universities by their OutDegree

     As above, the World network is the aggregated union of national sub-networks. The betweenness centrality index detects the gateway universities that connect these national sub-networks with the remaining ones. Table 4 shows the principal universities in each country according to the betweenness centrality. We can appreciate outstanding universities in each country such as MIT in the US, Cambridge in the UK or ETHZ in Switzerland. Thus, these universities connect local web spaces with international ones. However, there are no German or Spanish universities in the top positions, although both countries have a good position in the network. We suggest that as there is a linguistic factor in the relationships between countries, the German-speaking network is represented by ETHZ and the Spanish-speaking one by the Autonomous National University of Mexico (UNAM). Moreover, the betweenness index is rather close to the degree indicators, so we can state that these universities are the most important in their national or linguistic sub-network.

Table 4. First 10 universities by their Betweenness in their countries

     Discussion

     For some while now, the use of search engine data has been discussed because of the instability of their results over a short time period (Bar-Ilan, 1998; Rousseau, 1997), the weakness of their search operators (Igwersen, 1998) and the unreliability of their databases (Sullivan, 2003). However, recent studies have shown that current search engines have improved their consistency and reliability (Bar-Ilan, 2002; Bar-Ilan, 2004; Bar-Ilan, 2005a). Although their technical features have considerably improved, the coverage of their databases and the harvesting process are key issues to discuss. Bar-Ilan (2005b) detects that some search engines have serious problems indexing and retrieving non-Latin characters such as Japanese, Chinese or Russian. Vaughan and Thelwall (2004) showed that there is a local bias in favour of US and against East Asian web sites which are underrepresented in the search engines. Our work may be affected by these biases because large East Asian universities web domains are located far away in the graph (Figure 2), although they have a large amount of web pages. The great presence of the US universities may be slightly affected by these coverage biases as well. Interpreting these results must take into account these biases.
     The link flows and web page distribution in the geographical map (Figure 1) follow a similar pattern to the European Union (Ortega & Aguillo, 2008b). Countries with many web pages attract and make more links than others, confirming the strong relationship between web pages and links (Thelwall & Harries, 2003; Katz & Cothey, 2006). The network graph also shows similar results to previous works. The World-class universities are grouped in local or national sub-networks which are connected with other sub-networks for linguistic or geographical reasons (Heimeriks & van den Besselaar, 2006; Ortega et al., 2008). These local or national sub-networks are structurally fitted to the community model of the Web suggested by Flake et al. (2000; 2002), several “gateway” universities act as hubs/authorities that connect the national communities or sub-networks between them (Barabasi & Albert, 1999; Kleinberg, 1999). This causes the reduction of the distances between nodes and explains the emergence of small-world phenomena on the Web (Björneborn, 2003).

     Conclusions

     The World-class university network graph is comprised of national sub-networks that merge in a central core where the principal universities of each country pull their networks toward international link relationships. This network rests on the United States, which dominates the world network in conjunction with the aggregation of the European ones, especially the British and the German sub-networks. This situation may be caused mainly by the technological development of these countries and the production of international content, that is, English web pages. This second reason might explain the apparent backward situation of some East Asian countries.

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