This is what I have in my database, which seems to match:
1. John Hargreaves
sp: Mary
2. Richard Hargreaves (c.28 Nov 1802-Barnborough,Yorkshire;b.6 Feb 1883-Rawmarsh,Yorkshire,England)
sp: Mary (b.Abt 1808-Wath upon Dearne,Yorkshire;d.Abt 1888-Rotherham RD,Yorkshire)
3. Joseph Hargreaves (c.20 Aug 1837-Rawmarsh,Yorkshire,England)
sp: Fanny (b.Abt 1834-Balby,Yorkshire)
4. William Hargreaves (b.Abt 1864-Rawmarsh,Yorkshire,England)
4. Richard Hargreaves (b.Abt 1867-Rawmarsh,Yorkshire,England;d.1904-Wortley RD,Yorkshire)
sp: Lydia Martha Barker (b.26 Mar 1872-Rotherham,Yorkshire;m.26 May 1901;d.4 Aug 1907-RRD,Yorkshire)
4. Ann Hargreaves (b.1871-Rawmarsh,Yorkshire,England)
4. Wilfred Hargreaves (b.Abt 1875-Rawmarsh,Yorkshire,England)
3. Sarah Hargreaves (c.15 May 1842-Rawmarsh,Yorkshire,England)
sp: Luke Charlesworth (b.Abt 1841-Todmorden,Yorkshire;m.1863)
4. George Charlesworth (b.Abt 1870-Masbro,Yorkshire)
4. Annie Charlesworth (b.Abt 1874-Swinton,Yorkshire)
3. George Hargreaves (c.23 Aug 1846-Rawmarsh,Yorkshire,England)

Any corrections and additions would be much appreciated.
There might be a connection with earlier generations, but before my gggf William (that is his monument at Rawmarsh) they lived in the Wakefield, East Ardsley areas, and before William's father John (c1794-1835) I have only a guess as to who his parents were (possibly John Hargreaves and Ann Hartley). The miners in the Hargreaves family seem to have been a close-knit bunch, so they are probably all related somehow!

There is a concrete connection (by marriage) with the wife of Richard Hargreaves in your tree, Lydia Martha Barker - her first husband, Thomas Arthur Bamforth, was a nephew of my great grandfather Thomas Hargreaves.