The elders portrayed and discussed in the New Testament reveal men and women who were season believers and mature not only in the faith, but in life. They were in fact spiritual parents within the house churches. You will read of instances where there were disputes, where men like Peter and Paul and others of the itinerant kind, travelled all over the Mediterranean world equipping and releasing people to be who God called them to be. The would appoint elders in each town and city (see the Pastoral Epistles) and would advocate that disputes would be settled amicably and broken relationships restored. You need only to read the Book of Acts and the epistles to see all the unctions to deal with heart and relational issues. The elders would simply act on the behalf of all, be intermediaries in disputes and attempt reconciliation. They were very much like parents with children, and they were their to trouble shoot as well as encourage and motivate and protect.
In our house churches we seek to model this same kind of compassion, where eldership is a more seasoned elder brother who looks out for people and protect the local fellowship through mediation and reconciliation. They never control a gathering and have a title. It is a function, and it flows as naturally as parenting does in natural families.