Community structure in co-inventor networks affects time to first citation for patents

Table 4 Community-related differences in the time lag Δt₁ until first citation

		Infomap	Prop. Lbls.	Rand. Wlks.	Greedy	Louvain
In	raw data $\overline {\Delta t_{1}}$	19.4	19.7	20.8	21.6	21.7
	raw data $\widetilde {\Delta t_{1}}$	16	16	17	17	17
	raw data^{Footnote 3} Mo Δ t 1 $\phantom {\dot {i}\!}\text {Mo}_{\Delta {t}_{1}}$	0	0	10	10	12
	lognorm fit $\overline {\Delta {t}_{1}}$	18±2	18±2	18.8±0.9	19.5±0.9	19.5±0.9
	lognorm fit $\widetilde {\Delta {t}_{1}}$	16±1	16±1	16.7±0.7	17.4±0.7	17.4±0.7
	lognorm fit $\phantom {\dot {i}\!}\text {Mo}_{\Delta {t}_{1}}$	12±2	12±2	12.6±0.9	12±2	13.3±0.9
Out	raw data $\overline {\Delta {t}_{1}}$	24.6	24.5	24.8	24.7	24.7
	raw data $\widetilde {\Delta {t}_{1}}$	19	19	20	20	20
	raw data $\phantom {\dot {i}\!}\text {Mo}_{\Delta {t}_{1}}$	15	15	15	15	15
	lognorm fit $\overline {\Delta {t}_{1}}$	21.5±0.9	21.5±0.9	21.5±0.9	21.5±0.9	21.5±0.9
	lognorm fit $\widetilde {\Delta {t}_{1}}$	19.4±0.7	19.4±0.7	19.4±0.7	19.4±0.7	19.4±0.7
	lognorm fit $\phantom {\dot {i}\!}\text {Mo}_{\Delta {t}_{1}}$	15.3±0.9	15.4±0.9	15.3±0.9	15.3±0.9	15.4±0.9
	t-test full dataset	8.4	6.6	6.8	8.7	7.6
	av. t-score subset	2.9	1.7	1.7	2.3	2.6

The mean ($\overline {\Delta {t}_{1}}$), median ($\widetilde {\Delta {t}_{1}}$), and modal ($\phantom {\dot {i}\!}\text {Mo}_{\Delta {t}_{1}}$) values derived from the raw data for the empirically observed distributions of time until the first citation that is not a self-citation and either originates from within (In) or outside (Out) co-inventor communities are listed for community structures obtained using five different detection algorithms. Corresponding values derived from fits of the empirical distributions to log-normal form are also given for comparison. Welch’s t-test scores (Welch 1947) establish the statistical significance for the observed differences between mean time lags for in-community and out-of-community citations. We give t-values obtained from tests applied to the full datasets of in-community and out-of-community citation lags, as well as the average t-score found when comparing 500 independently and randomly chosen subsets of 300 citations from the in- and out-of-community datasets

		Infomap	Prop. Lbls.	Rand. Wlks.	Greedy	Louvain
In	raw data \(\overline {\Delta t_{1}}\)	19.4	19.7	20.8	21.6	21.7
	raw data \(\widetilde {\Delta t_{1}}\)	16	16	17	17	17
	raw data^{Footnote 3} Mo Δ t 1 $\phantom {\dot {i}\!}\text {Mo}_{\Delta {t}_{1}}$	0	0	10	10	12
	lognorm fit \(\overline {\Delta {t}_{1}}\)	18±2	18±2	18.8±0.9	19.5±0.9	19.5±0.9
	lognorm fit \(\widetilde {\Delta {t}_{1}}\)	16±1	16±1	16.7±0.7	17.4±0.7	17.4±0.7
	lognorm fit \(\phantom {\dot {i}\!}\text {Mo}_{\Delta {t}_{1}}\)	12±2	12±2	12.6±0.9	12±2	13.3±0.9
Out	raw data \(\overline {\Delta {t}_{1}}\)	24.6	24.5	24.8	24.7	24.7
	raw data \(\widetilde {\Delta {t}_{1}}\)	19	19	20	20	20
	raw data \(\phantom {\dot {i}\!}\text {Mo}_{\Delta {t}_{1}}\)	15	15	15	15	15
	lognorm fit \(\overline {\Delta {t}_{1}}\)	21.5±0.9	21.5±0.9	21.5±0.9	21.5±0.9	21.5±0.9
	lognorm fit \(\widetilde {\Delta {t}_{1}}\)	19.4±0.7	19.4±0.7	19.4±0.7	19.4±0.7	19.4±0.7
	lognorm fit \(\phantom {\dot {i}\!}\text {Mo}_{\Delta {t}_{1}}\)	15.3±0.9	15.4±0.9	15.3±0.9	15.3±0.9	15.4±0.9
	t-test full dataset	8.4	6.6	6.8	8.7	7.6
	av. t-score subset	2.9	1.7	1.7	2.3	2.6