The network in the graphical area spread over 1 km to 10 km or within a same building is known as:

LAN

The correct answer is Option (1) - LAN

LAN: Stands for Local Area Network and typically covers a limited geographical area, ranging from a single building or campus to a few kilometers. This aligns with the range you mentioned (1 km to 10 km).

VAN: Stands for Virtual Area Network and is a software-defined network that creates a logical network on top of a physical network. It doesn't have a specific geographical range.

MAN: Stands for Metropolitan Area Network and typically covers a larger area than a LAN, spanning a city or a metropolitan area. Its range is usually between 5 km and 50 km, exceeding the upper limit of your mentioned range.

WAN: Stands for Wide Area Network and covers a large geographical area, spanning across cities, states, or even countries. Its range is much larger than what you described.