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Increasing reliance on the electronic mail (e-mail) has attracted spammers to send more and more spam e-mails in order to maximizing their financial gains. These unwanted e-mails are not only clogging the Internet traffic but are also causing storage problems at the receiving servers. Besides these, spam e-mails also serve as a vehicle to a variety of online crimes and abuses. Although several anti-spam procedures are currently employed to distinguish spam e-mails from the legitimate e-mails yet spammers and phishes obfuscate their e-mail content to circumvent anti-spam procedures. Efficiency of anti-spam procedures to combat spam entry into the system greatly depend on their level of operation and a clear insight of various possible modes of spamming. In this paper we investigate directed graph model of Internet e-mail infrastructure and spamming modes used by spammers to inject spam into the system. The paper outlines the routes, system components, devices and protocols exploited by each spamming mode.