Brisbane’s small world
From Griffith REVIEW Edition 3: Webs of Power
© Copyright Griffith University & the author.
Written by Malcolm Alexander
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Malcolm Alexander's biography and other articles by this writer
Five years after audiences flocked to the movie Six Degrees of Separation, scientists rediscovered social networks. In June 1998, the leading scientific journal, Nature, published an article by two physicists, Duncan Watts and Steven Strogatz, that addressed the so-called small-world problem. This is the possibility, first suggested by Stanley Milgram's experiments in the 1940s, that the United States population was connected by only six degrees of separation.
The "small world" network model Watts produced unravelled this sociological conundrum and extended it to explain some mysteries of the biological world. Watts discovered small-world architectures in the network of connections between actors co-starring in the same movies, the US western states electricity grid and the neural connections of the "celebrated and much studied worm Caenorhabditis elegans". He applied the model to other areas – the spread of infections and the synchronisation of crickets' chirping. Since then connectivity and small-world networks have been discovered in many types of self-organising systems from ecology to computer programming.
Watts's small world showed that surprisingly few connections and connectors are needed to create a network. Sociologists had been studying networks since the 1930s, but Watts and Strogatz turned their thinking around.
Last year Lucy Butcher and I examined the boards of companies, public organisations and community organisations in Brisbane to see what a small-world social network looks like. We found a social network created by prominent citizens' participation on the boards of these organisations. In social-network analysis this is known as an affiliation network since people are associated not by direct links but by their affiliation with a corporate entity. The network connections between members of these boards are made by joint memberships (or "interlocking directors") of those holding positions on two or more boards. These are the network connectors.
In Brisbane there are 314 connectors who link a population of 1930 board members at just 4.68 degrees of separation. The network is grounded in public-sector advisory boards rather than private companies. This suggests how political patronage interacts with social prestige to weave the web of civil society into stable, but not permanent, structures of community power.
THE SMALL-WORLD MODEL HIGHLIGHTS unexpected consequences of small but familiar coincidences of social life. Most people have acquaintances or distant relatives who have contact with celebrity circles or public life. Such connections are a tiny, often inactive, part of our total social networks. Watts's small-world theory demonstrated how, like yeast in bread, this very small proportion of "long-distance" links can, in theory, connect very large populations at six degrees of separation or less. Long-distance connections of this kind jump across social distance and can traverse entire populations. It is conceivable that, somehow, they link everyone in the world to everyone else. The average degree of separation among the world's population is probably greater than the six degrees of separation suggested by Milgram, but not significantly greater. In practical terms, most people are unlikely to use such a chain beyond its second point, a friend of a friend.
Social networks model as mathematical graphs. In social networks people are the nodes and the connections between them the edges. Theorists found that random graphs connected quite suddenly, like water turning into ice, when the number of connections per person reaches a certain level. The number of edges needed to connect a large group does not increase directly with size: the proportion of edges necessary to connect 100 nodes is 4.6, yet 1000 nodes requires 6.9 and 1 billion nodes needs only 20.7. This explains why there may only be a few degrees of separation in very large populations.
Prior to Watts's work, random graphs had not seemed relevant to social networks or the small-world problem because people do not make social connections randomly. On the contrary, social connections are locally clustered and interactions within a circle of friends are reinforcing. It is common, when we meet a new person, to establish rapport by talking about "mutual" acquaintances. We explore and reinforce these connections rather than ones that go beyond the group. These are our "strong" ties or "bonds". Before Watts, social-network theorists assumed that these strong social ties precluded significant development of long-distance or "weak" social ties. Similarly, ties across distinct populations were considered rare. Milgram wondered how social paths would cross from black to white populations in the US of the 1940s. We might wonder how an average Tasmanian would link to someone in Namibia. Localism, parochialism, in-group conformity and similar social habits were thought to override the potential for network connectivity.
Watts's model shattered this barrier. He simulated graphs where all the points began by being clustered together in local groups. He then relaxed the clustering constraint creating links "rewired" at random, as in a random graph. He discovered that astonishingly small numbers of links need to be rewired to achieve short paths and fewer degrees of separation. A random rewiring would mean that while the population of Tasmania is clustered in local groups that connect with each other, a chance connection that links a Tasmanian to a Namibian links these two populations.
Thus, small-world connectivity can occur even when most time and energy is engaged with local circles and friendships. There is no trade-off between building local bonds and long-distance ties. One does not displace the other.
IN AN ACTIVE COMMUNITY, NETWORKS ARE PART of public life. Advisory boards, consultative committees and community organisations draw people into the public realm and provide meeting places for active citizens. Seen in isolation, these boards are small, localised groups whose members interact and come to know one another. However, there are a few people who serve on two or more boards. These are the networkers who, potentially, join otherwise separated groups of board members into a network.
Social-network analysts have worked with affiliation networks for many years. First they recognised the duality in these networks. Affiliation networks are, simultaneously, links between organisations and links among people. Because of the power and prominence of large corporations in business and public life, the most exhaustive studies of affiliation networks were by researchers dealing with networks of interlocking company directors. These studies focused almost exclusively on links between organisations. Recent interest in small-world networks has encouraged researchers to investigate corporate interlocking as a network of interpersonal connections. The results are striking, showing that connections between organisations are likely to follow from links between people, rather than the other way around.
Our investigation of the affiliation network of public boards and committees in Brisbane illustrates this duality. At one level, it is a network study. It is also the beginnings of a community-power study that seeks to identify decision-making elites.