Quantum entanglement cannot be unlimitedly shared among an arbitrary number of qubits. The degree of bipartite entanglement decreases as the number of entangled pairs in an N-qubit system increases. We analyze a system of N qubits in which an arbitrary pair of particles is entangled. We show that the maximum degree of entanglement (measured in the concurrence) between any pair of qubits is 2/N. This tight bound can be achieved when the qubits are prepared in a pure symmetric (with respect to permutations) state with just one qubit in the basis stare \0 > and the others in the basis state \1 >.
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