Diagnostics for main path analysis

Computes K-sensitivity of the key-route network and the Jaccard overlap between SPC- and SPLC-based key routes as a robustness check.

Usage

main_path_diag(
  A,
  weights = NULL,
  k_values = c(5L, 10L, 15L, 20L, 30L),
  k_jaccard = 10L
)

Arguments

A

A square, named, directed adjacency matrix in which A[i,j] > 0 means that paper j cites paper i.

weights

Output of traversal_weights() with method = "spc". Computed internally when NULL.

k_values

Integer vector of K values for the sensitivity table. Default c(5, 10, 15, 20, 30).

k_jaccard

Integer K used for the SPLC/SPC Jaccard comparison. Default 10L.

Value

A named list:

k_sensitivity

Data frame with columns K, n_nodes, n_edges, and new_nodes (marginal nodes added at each K).

splc_spc_jaccard

Numeric Jaccard overlap of node sets between SPLC- and SPC-based key routes at k_jaccard.

weight_summary

Summary statistics for nonzero edge weights.

n_sources

Number of source nodes.

n_sinks

Number of sink nodes.

total_log_paths

Log of the total number of search paths of weights.

Details

The K-sensitivity table shows how the size of the key-route network grows as more seed routes are added. Stabilisation of new-node counts signals that the main structural backbone has been captured.

The SPLC/SPC Jaccard overlap at k_jaccard routes measures whether the key routes change when the intermediate papers are also counted as origins of knowledge (SPLC) instead of only the sources (SPC), which is the main difference between the two weights (Liu, Lu and Ho, 2019). A value of one means that both weights give the same papers.

References

Liu, J.S., Lu, L.Y.Y. and Ho, M.H.C. (2019). A few notes on main path analysis. Scientometrics. 119(1): 379-391. doi:10.1007/s11192-019-03034-x .

Verspagen, B. (2007). Mapping technological trajectories as patent citation networks. Advances in Complex Systems. 10(1): 93-115. doi:10.1142/S0219525907000945 .

Author

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 1, 0, 0, 0,
  0, 0, 0, 1, 1, 0,
  0, 0, 0, 0, 1, 0,
  0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 1,
  0, 0, 0, 0, 0, 0
), byrow = TRUE, nrow = 6)
rownames(A) <- letters[1:6]
colnames(A) <- letters[1:6]

main_path_diag(A, k_values = c(1L, 2L, 3L))
#> $k_sensitivity
#>   K n_nodes n_edges new_nodes
#> 1 1       3       2        NA
#> 2 2       5       4         2
#> 3 3       6       6         1
#> 
#> $splc_spc_jaccard
#> [1] 1
#> 
#> $weight_summary
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   1.000   1.000   1.000   1.333   1.750   2.000 
#> 
#> $n_sources
#> [1] 1
#> 
#> $n_sinks
#> [1] 2
#> 
#> $total_log_paths
#> [1] 1.098612
#>