Fuelled by coffee and amphetemines, he’d turn up at colleagues’
houses, announcing that ‘my brain is open’. By the time he died in
1996, he’d published about 1,500 papers, with over eight thousand
co-authors.[55]
As well as building networks, Erdős was interested in researching
them. Along with Alfréd Rényi, he pioneered a way of analysing
networks in which individual ‘nodes’ were linked together at random.
The pair were particularly interested in the chance these networks
would end up being fully connected – with a possible route between
any two nodes – rather than split into distinct pieces. Such
connectedness matters for outbreaks. Suppose a network represents
sexual partnerships. If it’s fully connected, a single infected person
could in theory spread an STI to everyone else. But if the network is
split into many pieces, there’s no way for a person in one component
to infect somebody in another.
It can also make a difference if there is a single path across the
network, or several. If networks contain closed loops of contacts, it
can increase STI transmission.[56] When there’s a loop, the infection
can spread across the network in two different ways; even if one of
the social links breaks, there’s still another route left. For STIs,
outbreaks are therefore more likely to spread if there are several
loops present in the network.
Although the randomness of Erdős–Rényi networks is convenient
from a mathematical point of view, real life can look very different.
Friends cluster together. Researchers collaborate with the same
group of co-authors. People often have only one sexual partner at a
time. There are also links that go beyond such clusters. In 1994,
epidemiologists Mirjam Kretzschmar and Martina Morris modelled
how STIs might spread if some people had multiple sexual partners
at the same time. Perhaps unsurprisingly, they found that these
partnerships could lead to a much faster outbreak, because they
created links between very different parts of the network.