  Bi-partite entanglement in multi-qubit systems cannot be shared freely. The
rules of quantum mechanics impose bounds on how multi-qubit systems can be
correlated. In this paper we utilize a concept of entangled graphs with
weighted edges in order to analyze pure quantum states of multi-qubit systems.
Here qubits are represented by vertexes of the graph while the presence of
bi-partite entanglement is represented by an edge between corresponding
vertexes. The weight of each edge is defined to be the entanglement between the
two qubits connected by the edge, as measured by the concurrence. We prove that
each entangled graph with entanglement bounded by a specific value of the
concurrence can be represented by a pure multi-qubit state. In addition we
present a logic network with O(N2) elementary gates that can be used for
preparation of the weighted entangled graphs of N qubits.
