School gunmen are always pupils whose efforts to overcome their shyness have been shunned by their classmates.
This rejection is then transformed into anger and a loss of empathy for other people, a combustible combination.
Academics from Indiana University Southeast, in America, analysed the personalities of eight pupils who committed high school shootings between 1995 and 2004. The perpetrators were all male, aged between 14 and 18.
The list of their personal qualities was taken from detailed FBI reports into the personality traits of school shooters. These qualities were divided into the personal, such as lack of empathy, and the social, which included their relationships with peers. The academics found that the eight killers shared many personality traits.
All were isolated and socially withdrawn. They all had a history of being bullied, or of bullying others. And they all had very low tolerance of frustration.
These characteristics combine to create a personality type that the Indiana academics refer to as "cynically shy".
Like other withdrawn pupils, the cynically shy have a desire to develop strong social connections with their classmates. They want to have friends, but they lack the social skills to do so.
"The cynically shy represent a small, select group of individuals, who make the effort to move towards others but are rejected by them," the researchers said. "For such individuals, this rejection can manifest itself in a development of a sense of social disconnection."
This generates feelings of anger. This anger, in turn, can result in a tendency to dehumanise other people, losing all empathy for them.
"It has been suggested that this loss of empathy for and dehumanisation of others is characterised in the cynically shy by a strong hatred for others and feelings of superiority," the academics said.
"This combination of a lack of empathy and dehumanisation of others can be manifested in interpersonal acts of excessive violence, such as high school shootings."
All but one of the school gunmen analysed by the researchers expressed anger or violence in their schoolwork or their journals. And every one of them enjoyed violent films, video games and music.
Similarly, all they appeared to be alienated from their surroundings and their classmates. All but one revealed a tendency to dehumanise other people.
The more pupils disconnect from their classmates, losing any sense of empathy for them, the more likely it becomes that they will mistreat them in some way.
Schools and psychologists, therefore, need to work out how best to deal with pupils exhibiting traits of cynical shyness.
And the researchers called for an investigation into how these pupils' coping mechanisms differ from those of more traditionally shy classmates: why do they turn their shyness into anger?
Once this has been established, it may be easier to help them cope with the negative emotions that their shyness engenders, before it is too late.
In April 2007, while the research was still in progress, the worst school shooting in US history took place. Cho Seung-Hui went on a shooting spree at Virginia Tech, which left 32 people dead.
Although 23-year-old Cho was older than the other pupils studied by the Indiana academics, he displayed 23 of the 30 personality and social traits associated with the cynically shy.
The researchers said: "The incident also highlights the importance of future research, to better understand the dynamics associated with such behaviour."
- `High school shooters as cynically shy', by Kristin Terry Nethery and Bernardo J Carducci. www.ius.edushyness
Kip Kinkel: In May 1998, aged 15, he killed both his parents. The next day, he walked into Thurston High School, in Oregon, with a semi-automatic rifle. He killed two pupils, and wounded 25 others.
Before the shootings Kinkel regularly felt depressed and angry, often without knowing why, and set off explosives to vent these feelings. His sister described him as lonely, and said that he was "needing more kids his age to spend more time with".
Eric Harris and Dylan Klebold: In April 1999, this pair of 18-year-olds massacred 12 fellow pupils and a teacher at Columbine High School in Denver. They then turned their guns on themselves. Both teenagers had revealed an obsession with violence in their school creative writing. Harris had been attending anger management classes and taking medication. Klebold also had difficulty controlling his anger, and was known to swear at his teachers. But his diary revealed severe self-loathing.
Cho Seung-Hui: In April 2007, 23-year-old Virginia Tech student Cho Seung- Hui murdered 32 fellow students and wounded 25 others. He then committed suicide.
Cho's uncle claims that he did not mix much with others as a child. During middle school, he suffered from selective mutism, and was bullied about his shyness. A Virginia Tech tutor described him as awkward, lonely and insecure.