  We use the concept of \textit{entangled graphs} with weighted edges to
present a classification for four-qubit entanglement which is based neither on
the LOCC nor the SLOCC. Entangled graphs, first introduced by Plesch et al.
[Phys. Rev. A 67, (2003) 012322], are structures such that each qubit of a
multi-qubit system is represented as a vertex and an edge between two vertices
denotes bipartite entanglement between the corresponding qubits. Our
classification is based on the use of generalized Schmidt decomposition of pure
states of multi-qubit systems. We show that for every possible entangled graph
one can find a pure state such that the reduced entanglement of each pair,
measured by concurrence, represents the weight of the corresponding edge in the
graph. We also use the concept of tripartite and quadripartite concurrences as
a proper measure of global entanglement of the states. In this case a circle
including the graph indicates the presence of global entanglement.
