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Information-theoretic security constraints reduce the connectivity of wireless networks in the presence of eavesdroppers, which motivates better modeling of such networks and the development of techniques that are robust to eavesdropping. In this letter, we are concerned with the existence of secure connections from a typical transmitter to the legitimate receiver(s) over fading channels, where the legitimate nodes and eavesdroppers are all randomly located. We consider non-colluding and colluding eavesdroppers, and derive the network secure connectivity for both eavesdropper strategies. We mathematically show how nodes with multiple transmit antenna elements can improve secure connectivity by forming a directional antenna or using eigen-beamforming. Compared with single antenna transmission, a large connectivity improvement can be achieved by both multi-antenna transmission techniques even with a small number of antennas.