Here is all I found in the official docs:
Client-side events for socket.io object:
connect. Fired upon a successful connection.connect_error. Fired upon a connection error.
Parameters:Objecterror object
connect_timeout. Fired upon a connection timeout.reconnect. Fired upon a successful reconnection.
Parameters:Numberreconnection attempt number
reconnect_attempt. Fired upon an attempt to reconnect.reconnecting. Fired upon an attempt to reconnect.
Parameters:Numberreconnection attempt number
reconnect_error. Fired upon a reconnection attempt error.
Parameters:Objecterror object
reconnect_failed. Fired when couldn’t reconnect withinreconnectionAttempts
Client-side events for socket object:
connect. Fired upon connecting.error. Fired upon a connection error
Parameters:Objecterror data
disconnect. Fired upon a disconnection.reconnect. Fired upon a successful reconnection.
Parameters:Numberreconnection attempt number
reconnect_attempt. Fired upon an attempt to reconnect.reconnecting. Fired upon an attempt to reconnect.
Parameters:Numberreconnection attempt number
reconnect_error. Fired upon a reconnection attempt error.
Parameters:Objecterror object
reconnect_failed. Fired when couldn’t reconnect withinreconnectionAttempts
Server-side events:
connection/connect. Fired upon a connection.
Parameters:Socketthe incoming socket.
Edit:
For the current version (1.3.4) the reconnect_attempt and reconnecting
client-side events are synonyms.