 All these phase transitions are caused by the few richest vertices, which drift towards the SZG centre, providing most of the edges  .
<meaning-changed>  All these phase transitions are caused by the few richest vertices, which drift towards the SZG centre, providing most of the edges  .
 All these phase transitions are caused by the few richest vertices, which drift towards the SZG centre, providing most of the edges increasing the leader's degree .