A wireless mesh network is any wireless network where data is transmitted using mesh networking. That is, where nodes don't just send and receive data, but also serve as a relay for other nodes and each node collaborates in propagating data on the network.
A wireless mesh network can be thought of as a collection of nodes where each mesh node is also a router. Compare this to a WiFi access point where service can be provided only within reach of the signal and when it is turned off, the connection is gone. Mesh nodes work differently by rerouting data to another hop which it is connected to, bypassing the empty area where a node might be off.
The concept of mesh networking can be applied to both physical and wireless networking, but it's much more commmon for wireless networks given the cabling costs that would be required to implement as a physical topology.
A key difference here is that mesh nodes work in a cooperative gain scheme where the more nodes that are active, the greater the bandwidth available Consider this analogy in traditional networking: when cars (data) coming from a wide road comes to a small bridge they all have to slow down to wait in line. To increase the number of cars going through, you need to make a bigger bridge (add bandwidth) which is then wasted in times of less traffic. In mesh networking, imagine people coming to a river, where in order to continue each person drops a rock to make a foot bridge. The more people that needs to pass, the more rocks are thrown in. But if there are fewer users, then only a few rocks are needed. In other words, the bandwidth scales automatically based on the number of users.
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