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Whether it is a PR representative, a CEO or a top player in your target industry, they have to deal with sycophantic communication every day. If you contact one of them directly with an express intention to plead for work, a positive response is unlikely.
Be friendly, appear interested, and don't push yourself forward -- simply by being connected through social networking opportunities will find themselves in your news feed. Be strategic in who you follow, re-tweet updates that interest you, and contribute to discussions.
There is no reason why online networking has to remain strictly online. If you follow events, conferences and talks relating to your field, it is possible that you may meet those you are already in contact with -- taking your job search a step further.
Lists, which can be found on your profile page, can be a useful feature to both supplement your Twitter following and also to find the most relevant users to follow in your field. In the same manner, if your Tweeted content is relevant and insightful, eventually you will be added to specific lists by other users to find.