I am trying to evaluate the current police stations. so I want to find the mean point of crime points in the city and compare the OD cost matrixes of the results. Is there any way to find the mean centre of points on a network?
For 2D case there are many options possible. One of them is arithmetic mean as per @Spacedman comment. I prefer very elegant peel away techinque by @whuber
As one can see for the pattern of 'crimes' I've used the results are very close. Note you cannot use weight (more than 1 crime in the same place) using peeling.
In case of network I don't see any other way but going through all network nodes and picking one that meets your criteria
In this case criteria is a minimum total distance of travel, perhaps total of squares is better. I guess it can be done using Network Analyst. I used networkx python package. Network shown has 2951 nodes and 3761 links (62 scenes). It took 45 mins on my rather solid machine. Time can be reduced using multi-processing