Flow ($\theta$)

A flow is an antisymmetric function on directed edges whose divergence of a flow vanishes away from designated sources and sinks.

The divergence of a flow at a vertex is its total outward flow. Flow conservation means that this divergence vanishes at every interior vertex.

The strength of a source-to-sink flow is the net amount leaving the source, equivalently the net amount entering the sink.

For unit edge resistances, the energy of a flow iswhere every unoriented edge is counted once.

An infinite locally finite connected graph is a transient graph exactly when it supports a unit flow from a vertex to infinity with finite energy of a flow.