Router
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Router is a networking device that connects multiple computer networks together, and directs network traffic between them. It uses IP addresses to make decisions on how to forward data packets across networks.
Router is a type of gateway, which is an entry point or exit point between two different networks. It acts as a bridge, translator, or the central point of connection, it enables and manage the flow of network traffic within a computer network.
As explained in routing, routers keep track information about network addresses in database called routing tables, it helps to determine where to send packets. They examine the destination's IP address of incoming packets and consult their routing tables to determine the appropriate next-hop router or network interface to forward the packets.
Routers are commonly used in homes, offices, and other environments to enable communication between devices on different networks. Routers can be wired or wireless, depending on the type of network they are connecting. Wired routers typically have Ethernet ports to connect devices via Ethernet cables, while wireless routers have built-in Wi-Fi capabilities to enable wireless connectivity for devices such as laptops, smartphones, and tablets.
In addition to forwarding data packets, routers can perform other functions such as network address translation (NAT), which allows multiple devices on a local network to share a single public IP address by using private IP address. Also, fire walling, which provides security by filtering and controlling network traffic.
Source: https://www.mytechlogy.com/IT-blogs/22654/essential-settings-for-home-network-routers/
Find out more about how routers forward or send data to another routers here
Hub & Switch vs Router
Hub and switch are networking device used for local or private network, it can't send data to external network. This is because hub and switch doesn't have public IP address, as you need it to communicate with external network like internet.
A network may have hub or switch to connect the local device and have a router to externally connect with other network. Data transmission from the local network won't be forwarded to external network by router. Only if the local device wants to send it outside using the destination IP address.
Hubs and switches can be thought as the device you use to make network, while routers are used to connect them.
Source: https://youtu.be/1z0ULvg_pW8?si=GkDgO98d3d0uKt43&t=401