100 Anna C. F. Collar
connections between local clusters that would otherwise remain separate. This combi-
nation of local clustering and long-distance links creates the “small-world” (Watts and
Strogatz 1998).
Because weak ties connect their clusters, the distance between two individual nodes,
even though they may be in remote clusters, is never very great: the network has ashort
path lengthbetween nodes. Furthermore, the weak ties can have the effect of joining up
each small, separate cluster into one, enormous, fully interconnected cluster—known in
physics as thegiant component(Watts 2003: 45–6). When this level of interconnection
is present, events on one side of the network will eventually percolate across to the other
side—in other words, there is the potential for full network diffusion. Granovetter found
that weak ties in a social network were instrumental in spreading information of which
our local network is not already aware. This is because strong ties have a highly localized
quality—these are our closest neighbors. Information that requires a higher degree of
trust in order to be adopted and spread further is better diffused through strong ties
(Shi, Adamic, and Strauss 2006; Collar 2013b; see Rogers 1995 for a full discussion
of innovations). We must remember too thateverybodyis both a weak and a strong tie,
that identification as such depends on perspective, and that classifications are subject
to change.
Applied to past scenarios, the small-world network has been used as a metaphor to
describe the changing configurations between close-knit kin groups and the use of codi-
fied material culture between the Epipaleolithic and Neolithic periods, as well as primate
societies and human evolution (Coward 2010). Malkin sees the Archaic Greek world of
colonies andmetropoleisas a small world (2003, 2011). This network structure is partic-
ularly robust—because nodes are often directly connected to one another, the removal
of a node at random is likely not to have too great an effect on the connectivity of the
network as a whole.
Scale-Free Networks
An important development resulted from the discovery by Albert and Barabási, that the
connectivity of many real-world networks is very skewed (1999). This means that the
majority of nodes are poorly connected, while a few are massively so—the network fea-
tures, for example, people who know “everybody” or airports central to global flight
patterns. Through the mechanism of preferential attachment (where a node receives con-
nections because it already possesses connections), certain nodes grow to be much larger.
This results in apower law, the graphic representation of many small nodes coexisting with
a few very large ones. Power law networks have “hubs,” nodes that are disproportionately
well connected—and form what are known asscale-freenetworks.
Because they possess a much higher number of links, hubs are incredibly powerful.
They are in control of the channels of information diffusion—whether this is charac-
terized as positive or negative. A hub can be central to the spread of a disease or an