I am trying to model Ip adress to cretae a fraud detection framework. So I am wondering if Ip Adress is a continuous or discrete or categorical variable. Bests
IP addresses are discrete. There is finite number of IP addresses and there are no useful meaning to adding and subtraction of IP addresses.
Having said that, you can define similarity between IP addresses. I simple example of similarity is to split the addresses into internal addresses vs. external addresses. You can go further and assign higher similarity to IPs belonging to the same subnet.
Please be aware that IP similarity definition might be very complex and problem dependent. For example, in many cases you are not interested in the country associated to IP. The complex similarity make it difficult to use it in algorithms in a straight forward way.