"The child's mother called me and described her symptoms," he said.
"She told me she had developed an obsession with the device and would ask for it constantly. She was using it three to four hours every day and showed increased agitation if it was removed."
Dr Graham said that young technology addicts experienced the same withdrawal symptoms as alcoholics or heroin addicts when the devices were taken away.
He warned that the condition prevented young people from forming normal social relationships, leaving them drained by the constant interaction.
"Children have access to the internet almost from birth now," he told the Sunday Mirror. "They see their parents playing on their mobile devices and they want to play too. It's difficult, because having a device can also be very useful in terms of having a reward, having a pacifier. But if you don't get the balance right it can be very dangerous.
"They can't cope and become addicted, reacting with tantrums and uncontrollable behaviour when they are taken away. Then as they grow older, the problem only gets worse."
Parents who have been unable to wean their children off computer games and mobile phones are paying up to £16,000 ($28,800) for a 28-day "digital detox" programme designed by Dr Graham at the Capio Nightingale clinic in London.
Psychiatrists estimate that the number of people who have become digitally dependent has risen by 30 per cent over the past three years.
A survey last week revealed that more than half of parents allowed their babies to play with their phone or tablet device. One in seven of more than 1000 parents questioned by babies.co.uk said they let them use the gadgets for four or more hours a day.
James Macfarlane, managing director of the website, said: "Given that babies between 3-12 months are awake for only around 10 hours per day this is a huge proportion of their waking day.
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