Applies an exponential temporal decay to the arcs of a citation adjacency matrix and optionally normalises the result so that each citing paper distributes exactly one unit of citation influence among its references.
Arguments
- A
A square, named, directed adjacency matrix.
- years
Named numeric vector of publication years aligned with row/column names of
A.- lambda
Positive numeric decay rate. Default
0.2.- normalize
Logical; if
TRUE(default) each column is divided by its sum so that the references of each citing paper sum to one.
Value
A numeric matrix of the same dimensions as A containing the
decay-weighted (and optionally normalised) citation arc weights.
traversal_weights uses only whether each arc is present, so
these weights do not change the search path counts; they can be combined
with them, for instance by multiplying the two matrices element by element.
Details
As in traversal_weights, A[i,j] > 0 means that paper
j cites paper i. The weight of the arc \(i \to j\) is
\(\exp(-\lambda \cdot (y_j - y_i))\) where \(y_i\) and \(y_j\) are
the publication years of \(i\) and \(j\) respectively. A larger
\(\lambda\) discounts older citations more aggressively. The
normalisation divides each column, which holds the references of a citing
paper, by its sum, so that differences in the length of the reference lists
do not inflate the raw weights.
References
Hummon, N.P. and Doreian, P. (1989). Connectivity in a citation network: The development of DNA theory. Social Networks. 11(1): 39-63. doi:10.1016/0378-8733(89)90017-8 .
Examples
# P1 is cited by P2 and P3, which are both cited by P4
A <- matrix(c(
0, 1, 1, 0,
0, 0, 0, 1,
0, 0, 0, 1,
0, 0, 0, 0
), byrow = TRUE, nrow = 4)
rownames(A) <- c("P1", "P2", "P3", "P4")
colnames(A) <- c("P1", "P2", "P3", "P4")
years <- c(P1 = 2000, P2 = 2005, P3 = 2006, P4 = 2010)
citation_decay(A, years, lambda = 0.2)
#> P1 P2 P3 P4
#> P1 0 1 1 0.000000
#> P2 0 0 0 0.450166
#> P3 0 0 0 0.549834
#> P4 0 0 0 0.000000