Parity Peers – What Do the 3 Different Peer Numbers Represent in Parity

The peer discovery algorithm is based on the kademlia protocol.

More details: https://github.com/ethereum/devp2p

A standalone implementation can be found here.

Edit:

A simplified model of how the p2p algorithm works is the following:

• you have nodes that are assumed to be always available/online (in Ethereum they are called bootstrap nodes)
• bootstrap nodes maintain a list of all nodes that connected to them in a period of time (predefined temporal value, for example last 24 hours)
• when peers (Ethereum client applications such as eth, geth, pyethapp, etc.) connect to the Ethreum network, they first connect to the bootstrap nodes which share the lists of peers that have connected to them in the last predefined time period
• the connecting peers then synchronize with the peers and may prune the connections to the bootstrap nodes since they are no longer essential in peer discovery (the peers can perform discovery on their own)

Active versus connected is just a terminology question: Active means, they are actively synchronizing the chain, a 0 basically means you are already fully synchronized (or have no peers at all). Connected are all peers which you are listing to for new blocks and transactions, ideally this should be not 0.

You say, you have two nodes with 0/1/25 and one with 0/2/25, so your (virtual) peer-to-peer network looks like this:

[0/1/25] --- [0/2/25] --- [0/1/25]

So you have one node connected to the other two nodes, while they are not connected to a ring. Try to add all three enode addresses to a reserved peers file and pass this to all of your nodes:

--reserved-peers FILE          Provide a file containing enodes, one per line.
                               These nodes will always have a reserved slot on top
                               of the normal maximum peers. (default: None)