Before revision:  We show that hierarchical connectivity is persistent in the quasi-critical regime associated with optimal processing capabilities and normal brain function (Griffiths phase) and breaks down in states deviating from this regime , often associated with pathological conditions.
After revision:  We show that hierarchical connectivity appears in functional networks in a persistent way if the dynamics is set to be in the quasi-critical regime associated with optimal processing capabilities and normal brain function (Griffiths phase) and breaks down in states deviating from this regime , often associated with pathological conditions.