Description Usage Arguments Author(s) References See Also Examples

This function computes the relatedness between entities (industries, technologies, ...) from their co-occurence (adjacency) matrix. Different normalization procedures are proposed following van Eck and Waltman (2009): association strength, cosine, Jaccard, and an adapted version of the association strength that we refer to as probability index.

1 | ```
relatedness(mat, method = "prob")
``` |

`mat` |
An adjacency matrix of co-occurences between entities (industries, technologies, cities...) |

`method` |
Which normalization method should be used to compute relatedness? Defaults to "prob", but it can be "association", "cosine" or "Jaccard" |

Pierre-Alexandre Balland p.balland@uu.nl

Joan Crespo J.Crespo@uu.nl

Mathieu Steijn M.P.A.Steijn@uu.nl

van Eck, N.J. and Waltman, L. (2009) How to normalize cooccurrence data? An analysis of some well-known similarity measures, *Journal of the American Society for Information Science and Technology* **60** (8): 1635-1651

Boschma, R., Heimeriks, G. and Balland, P.A. (2014) Scientific Knowledge Dynamics and Relatedness in Bio-Tech Cities, *Research Policy* **43** (1): 107-114

Hidalgo, C.A., Klinger, B., Barabasi, A. and Hausmann, R. (2007) The product space conditions the development of nations, *Science* **317**: 482-487

Balland, P.A. (2016) Relatedness and the Geography of Innovation, in: R. Shearmur, C. Carrincazeaux and D. Doloreux (eds) Handbook on the Geographies of Innovation. Northampton, MA: Edward Elgar

Steijn, M.P.A. (2017) Improvement on the association strength: implementing probability measures based on combinations without repetition, *Working Paper, Utrecht University*

`relatedness.density`

, `co.occurence`

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
## generate an industry - industry matrix in which cells give the number of co-occurences
## between two industries
set.seed(31)
mat <- matrix(sample(0:10,36,replace=T), ncol = 6)
mat[lower.tri(mat, diag = TRUE)] <- t(mat)[lower.tri(t(mat), diag = TRUE)]
rownames(mat) <- c ("I1", "I2", "I3", "I4", "I5", "I6")
colnames(mat) <- c ("I1", "I2", "I3", "I4", "I5", "I6")
## run the function
relatedness (mat)
relatedness (mat, method = "association")
relatedness (mat, method = "cosine")
relatedness (mat, method = "Jaccard")
``` |

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