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Table 10.1 Types of networks and some examples
Directed Nondirected

Unweighted Nodes: articles Nodes: scientific journals
(0-1) Links: direct citations Links: having the same
publisher
Nodes: scientists Nodes: articles
Links: from supervisor to Links: bibliographically
(former) Ph.D student coupled or not
Valued or Nodes: scientists Nodes: authors
weighted Links: citations given, Links: being coauthors,
weighted by number of weighted by the number
citations of coauthorships
Nodes: articles Nodes: journals or articles
Links: citations, weighted by Links: being cocited,
the time between weighted by the number
publication and citation of times

is equal to infinity (N). In undirected networks d G (s,t) 5 d G (t,s), for every
s and t in V.
One may distinguish two types of directed networks: one in which
cycles do not occur i.e., if there is a path from u to v, then there certainly
isn’t a path from v to u, and a second type for which this restriction does not
play. “Normal” citations between articles are of the first type: If article a
cites article b, then normally article b does not cite article a. If it does hap-
pen that a is linked to b, b is linked to c, and so on ending with a node that is
linked to a, this construction is called an Escher staircase, because of its
resemblance to the famous Escher lithograph “Ascending and descending.”
Such an Escher staircase is relatively easy to find between sites on the
Internet (Rousseau & Thelwall, 2004), but Rousseau and Small (2005)
even provide an example of a giant Escher staircase for article citations.

10.1.4 Definition of Cliques and Components

Cliques: A clique in a graph is a subgraph in which any node is directly
connected to every other node of the subgraph.

Components: A component of a graph is a subgraph with the characteris-
tic that there is a path between any two nodes in the subgraph and there is
no path between a node in the component and any node not in the com-
ponent. If the whole graph forms one component it is said to be totally
connected. Otherwise it is said to be unconnected.