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Since version 1.4 you receive a notification when a new device is connected to your network, even when you are not using your device at that moment. You have also a register with all notifications sent so you can check when any device has connected to your network even if you shut down your device.
Do you want to find out which devices are connected to your Wifi, so you can discover if somebody not supposed to be there is connected to your wireless network ?
With "Wifi Watch" you can scan your network for all reachable devices (not only the wireless, also the wired ones), and even more, you can monitor automatically when they connect/disconnect, as the app checks automatically (only if you want, you can disable it).
You can also check out the IPs, names (hostname), MAC addresses and Manufacturers of the devices currently or recently connected (the Manufacturer is actually the one who made the network card of the device, sometimes will be the same one of the device itself, sometimes will be different), so even if they are not using the network right now, but they used it lately, you will have this info (Anyway, your router must be capable of it).
* Translated to Italian thanks to @teoincontatto