These networks of relationships span companies, industry sectors and even countries, creating an informal web of contacts, knowledge and influence.

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But the Vatican may wield influence through complex cross-shareholdings and informal arrangements, although it denies this.

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An informal arrangement that gives Mr Clegg's party great influence on economic policy but relatively little on matters of security may be enough to keep the coalition a happy ship.

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The fourth kind of empire, suggests Mr Darwin, was a more informal one in places such as Argentina and Egypt where British influence was exercised through commerce, investment and shrewd diplomacy (occasionally of the gunboat kind).

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