Page 133 - Becoming Metric Wise

124 Becoming Metric-Wise

Figure 5.3 A citation network.

Table 5.4 The adjacency matrix of Fig. 5.3
d 1 d 2 d 3 d 4 d 5 d 6
0 1 1 1 0 0
d 1
0 0 0 1 1 0
d 2
0 0 0 1 0 1
d 3
0 0 0 0 0 1
d 4
0 0 0 0 0 0
d 5
d 6 0 0 0 0 0 0
Table 5.5 Representation of the network of Fig. 5.3 by a list of outlinks
Citing document Cited document
d d 2 , d 3 , d 4
d 2 d 4 , d 5
d 3 d 4 , d 6
d 4 d 6

the citing document d i and the column to the cited document d j . Fig. 5.3
and Table 5.4 illustrate this, where an arrow means “cites.”
Of course, it is also possible to reverse the arrows to obtain the graph
of the relation “is cited by.” The adjacency matrix of this new graph is
merely the transpose (exchange rows and columns) of the adjacency
matrix of the citation network of the “cites” relation. Another representa-
tion consists in just listing all outlinks, see Table 5.5. As a real-world cita-
tion network is often very sparse (many empty cells in the matrix) this
third method is often a parsimonious representation.