Database Reference
In-Depth Information
Albert (1999) introduced the scale-free model (or BA model) by viewing the
network as a dynamical object that evolves with addition of nodes and links to
the system, in strong contrast to the static models that dominated the literature
before. Imagine an initial network of a small number of nodes
m
0
. At each time
step we add a new node with
m
edges that links the node to
m
different vertices
already present in the network. The probability that a new node will be con-
nected to node
i
depends on the connectivity
k
i
of that node. After
t
time steps
the model leads to a network with
t
+
m
0
nodes and
mt
edges. This network
evolves into a scale-invariant state with the probability that a node has
k
edges
following a power law with exponent
γ
=
3.
In addition to the measures listed above, the concept of
tie strength
has
attracted particular attention in the study of social networks. It was introduced
by sociologist Mark Granovetter in 1973 as a “combination of the amount of
time, the emotional intensity, the intimacy (mutual confiding) and the reciprocal
service which characterize the tie.” He proposed a model of society consisting
of small and fully connected circles of friends, linked by strong ties. Weak ties
connect the members of these intimate circles to their acquaintances, who have
strong ties to their own friends. Since weak ties act as bridges between separate
“social micro-worlds,” they play a crucial role in any number of social activities,
such as the spreading of information, ideas, and diseases, or in finding a job.
Conversely, strong ties link persons in intimate and tight communities, affecting
emotional and economic support.
The existence of a local coupling between tie strengths and network topology
is confirmed by recent research, which exploits the huge quantity of human
interactions recorded by modern tools and technologies. A study conducted by
Onnela et al. analyzed a huge data set that stores the mobile phone interac-
tion of millions of individuals in a time period of 18 weeks. The researchers
inferred a social network from data connecting two users with a link if there had
been at least one reciprocated pair of phone calls between them, and defining the
strength of a tie as the aggregated duration of calls. Consistent with Granovetter's
hypothesis, the majority of the strong ties were found within highly connected
communities, indicating that users tend to talk for most of their time with the
members of their immediate circle of friends. In contrast, most links connect-
ing different communities were weaker than the links within the communities.
Moreover, as a consequence of the topological structure of the network, remov-
ing the weakest links leads to a rapid network's sudden disintegration, while
removing first the strongest ties shrinks the network but will not precipitously
break it apart.
The interesting findings discovered by the Onnela et al. study, together with
those of more recent works, confirm the importance of tie strength in study of
networks, suggesting that weak and strong ties play a different but crucial role
in the understanding of many dynamic processes regarding our society.
