Calculate the k and g functions for a set of points on a network (maturing).

```
kfunctions(
lines,
points,
start,
end,
step,
width,
nsim,
conf_int = 0.05,
digits = 2,
tol = 0.1,
resolution = NULL,
agg = NULL,
verbose = TRUE,
return_sims = FALSE
)
```

- lines
A feature collection of linestrings representing the underlying network. The geometries must be simple Linestrings (may crash if some geometries are invalid) without MultiLineSring

- points
A feature collection of points representing the points on the network. These points will be snapped on their nearest line

- start
A double, the lowest distance used to evaluate the k and g functions

- end
A double, the highest distance used to evaluate the k and g functions

- step
A double, the step between two evaluations of the k and g function. start, end and step are used to create a vector of distances with the function seq

- width
The width of each donut for the g-function. Half of the width is applied on both sides of the considered distance

- nsim
An integer indicating the number of Monte Carlo simulations to perform for inference

- conf_int
A double indicating the width confidence interval (default = 0.05) calculated on the Monte Carlo simulations

- digits
An integer indicating the number of digits to retain from the spatial coordinates

- tol
When adding the points to the network, specify the minimum distance between these points and the lines' extremities. When points are closer, they are added at the extremity of the lines

- resolution
When simulating random points on the network, selecting a resolution will reduce greatly the calculation time. When resolution is null the random points can occur everywhere on the graph. If a value is specified, the edges are split according to this value and the random points can only be vertices on the new network

- agg
A double indicating if the events must be aggregated within a distance. If NULL, the events are aggregated only by rounding the coordinates

- verbose
A Boolean indicating if progress messages should be displayed

- return_sims
a boolean indicating if the simulated k and g values must also be returned as matrices

A list with the following values :

plotk A ggplot2 object representing the values of the k-function

plotg A ggplot2 object representing the values of the g-function

values A DataFrame with the values used to build the plots

The k-function is a method to characterize the dispersion of a set of points. For each point, the numbers of other points in subsequent radii are calculated. This empirical k-function can be more or less clustered than a k-function obtained if the points were randomly located in space. In a network, the network distance is used instead of the Euclidean distance. This function uses Monte Carlo simulations to assess if the points are clustered or dispersed, and gives the results as a line plot. If the line of the observed k-function is higher than the shaded area representing the values of the simulations, then the points are more clustered than what we can expect from randomness and vice-versa. The function also calculates the g-function, a modified version of the k-function using rings instead of disks. The width of the ring must be chosen. The main interest is to avoid the cumulative effect of the classical k-function. This function is maturing, it works as expected (unit tests) but will probably be modified in the future releases (gain speed, advanced features, etc.).