Each article contains internal links to other articles. This naturally endow Wikipedia with an oriented graph structure.

Specifically, we only consider human written internal links. This exclude link to other MediaWiki sites (such as other language editions or the Wiktionary), and automatically generated link (such as link to categories or dates). We also only consider articles, and not meta or discussion pages.

The data comes from the following revision of Wikipedia:
enwiki-latest-pages-articles.xml (90,722,896,813 bytes, md5:4ea802eb02577abe4624b3508d9f6c04) and
frwiki-latest-pages-articles.xml (5,599,729,496 bytes, md5:e279ca5aa85e7a9962836d310780cd0d) .

The relevant source code is available here.

Although the vast majority of article are strongly connect (we can go back and forth any article), some are isolated. These isolated group can be either fully disconnected, link to article of the main group without being linked back, or be linked without linking to the main group. Grouping articles by strongly connected components, we can find the following repartition:

Number of strongly connected components with respect to their size. Logarithmic scale.

Number of large strongly connected components with respect to their size. Linear scale.

The majority of these are fully disconnected, almost empty, article or placeholders. Among the groups with actual content, we mostly find articles on really specific subject, referencing some things on the main group but never cited anywhere.

There is some noteworthy large group. On the English edition:

• 35 seasons of a football club: 1922 Wisła Kraków season
• 33 football teams: 1962 All-East football team
• 26 lists of genera of Noctuidae: List of noctuid genera:A (which is not generated automatically)
• 18 pages of disambiguation about Dobrzyń: Dobrzyń
• 17 seasons of ice hockey: 1919–20 RPI men's ice hockey season
• 16 finales of a Japanese football cup: 1983 JSL Cup final

• 25 galaxies of the Andromeda and Triangulum constellation: Group of NGC 669
• 17 genus of fossil spider: Paurospina
• 16 galaxies of the Cetus constellation: Group of NGC 585
• 16 spider species: Fufius candango
• 14 seasons of basket : 2013-2014 Chicago Bulls season

If we restrict ourself to the main group, we can also answer an important question: Can we always go to 2731583 in less than 3 clicks? The answer is no, but we can in 6:

Number of article at a given distance of the article 2731583 (English edition) or 1696582 (French edition). Logarithmic scale.

The longest path for the English edition is:
Oppo Neo 3→Oppo Neo 5→ Oppo Neo 7→Bronze mirror→ Ancient Egypt→Napoleon.
Regarding the French edition, the longest path is:
Giant-cell carcinoma of the lung, Large-cell lung carcinoma→ Carcinome neuroendocrine à cellules géantes du poumon→ Large cell neuroendocrine carcinoma of the lung→ Myasthenia gravis→ Germany.

Finally, we can ask ourself if this is possible for another article? Unfortunately, computing the eccentricity is quit expense (it roughly takes 1.6sec), and cannot realistically be done for each article. We had to only consider a large sample of 324000 articles, and found the following eccentricities:

Eccentricities of a sample of de 324000 articles. Logarithmic scale.

To get a better understanding of how eccentric each article really is, we also looked at the number of article at a maximal distance for each possible eccentricity:

Number of articles realizing the eccentricity for each possible eccentricity value (minimum, maximum, mean, standard deviation). Linear scale.

The articles with a really high (more than 20) eccentricity are: Morning Musume Concert Tour 2009 Yomiuri ~Land East Live, Week 24, Albert Assor, 1897–98 Yale Bulldogs men's ice hockey season, Ooni Ojigidiri, 1997 in Ecuadorian football.