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Social Network Analysis

A social spirograph capturing the linkages within a social graph of 400 hundred friends.

A social spirograph capturing the linkages within a social graph of 400 hundred friends.

Social network analysis is the application of network theory to the modeling and analysis of social systems. It combines both tools for analyzing social relations and theory for explaining the structures that emerge from distributed social interactions. With the rise in computation and the emergence of a mass of new data sources, social network analysis is beginning to be applied to all types and scales of social systems from international politics to local communities and everything in between, as it increasingly finds application across the social sciences.

Networks & Statistical Analysis

Traditionally when studying societies we think of them as composed of various types of individuals and organizations. We then proceed to analyze the properties of these social entities such as their age, occupation or population, and then ascribe quantitative value to them. This allows social science to use the formal mathematical language of statistical analysts to compare the values of these properties and create categories such as low income households or generation X. We then search for quasi cause and effect relations that govern these values. This component-based analysis is a powerful method for describing social systems. Unfortunately though, it fails to capture the most important feature of social reality, that is the relations between individuals.
Statistical analysis presents a picture of individuals and groups isolated from the nexus of social relations that give them context. We can only get so far by studying the individual, because when individuals interact and organize, the results can be greater than the simple sum of its parts. It is the relations between individuals that create the emergent property of social institutions. And thus, to understand these institutions we need to understand the networks of social relations that constitute them. Ever since the emergence of human beings, we have been building social networks. We live our lives embedded in networks of relations. The shape of these structures and where we lie in them all affect our identity and perception of the world.1


Social network analysis is now one of the major paradigms in contemporary sociology, and is also employed in many other social sciences, it offers us a powerful formal language with which to model and analyze the structure of social relations and how this structure defines the overall social system. The big idea is that of connectivity, a central axiom of the social network approach to understanding social interaction is that social phenomena should be primarily investigated through the properties of relations between and within units, instead of the properties of these units themselves.
Connectivity creates a certain type of space. We are used to a linear conception of space, what is called a Euclidean space, it is the world we walk around in everyday and see all these people and things that have certain properties to them, but now imagine you pull out your mobile phone and it is almost as easy to call a person just next door as it is to call someone on the other side of the planet, this is a new kind of space where our traditional linear conception of space is being stretched and distorted by this connectivity.  Connectivity creates a nonlinear type of space and that space is better called a topology. Topology is a branch of mathematics that can be used to abstract the inherent connectivity of objects while ignoring their detailed form. In its most general definition topology means the way in which constituent parts are interrelated or arranged.2 Thus for any set of things or people we can have a different set of global rules for how they are interrelated.

Social networks

The rise of online social networks has provided researchers with a wealth of new data sources, making research in social networks a highly accessible activity

The rise of online social networks has provided researchers with a wealth of new data sources, making research in social networks a highly accessible activity

A social network is a system made up of a set of social actors such as individuals or organizations, and a set of ties between these actors that might be relations of friendship, work, colleagues or family. Social network science then analyzes empirical data and develops theories to explaining the patterns observed in these networks. In so doing we can begin to ask questions about the degree of connectivity within a network, its overall structure, how fast something will diffuse and propagate through it, or the influence of a given node within the network. Social network analysis has been used to study the structure of influence within corporations. Where traditionally we see organizations of this kind as hierarchies, by modeling the actual flow of information and communications as a network we get a very different picture, where seemingly irrelevant employees within the hierarchy can in fact have significant influence within the network.3

Network Dynamics

Researchers also study innovation as a process of diffusion of new ideas across networks, where the overall structure to the network, its degree of connectivity, centralization or decentralization are a defining feature in the way that innovation spreads or fails to spread. Network dynamics, that is, how networks evolve over time is another important area of research. For example, within law enforcement agencies social network analysis is used to study the change in structure of terrorists groups to identify changing relations through which they are created, strengthened and dissolved. Social network analysis has also been used to study patterns of segregation and clustering within international politics and culture. By mapping out the beliefs and values of countries and cultures as networks, we can identify where opinions and beliefs overlap or conflict.4


Social network analysis is a powerful new method we now have that allows us to convert often large and dense data sets into engaging visualization that can quickly and effectively communicate the underlying dynamics within the system. By combining new discoveries in the mathematics of network theory with new data sources and our sociological understanding, social network analysis is offering huge potential for a deeper, richer and more accurate understanding of the complex social systems that make up our world.

Social Networks

An example of a social network taken from a twitter community

An example of a social network taken from a twitter community

A social network is a model of a social system as consisting of nodes, that represent social actors and edges that represent the relations between these actors. Social networks come in many different kind, they may be physical where we are talking about basic demographics, the movement of people, migration, the spreading of viruses, urban transportation etc. they may be economic networks representing financial and economic connections. They may be political networks through which power flows, a cultural network through which beliefs, values and ideologies flow.


Social networks can be analyzed by either taking a micro level bottom up perspective where we look at the agents, why and how they make connections or a more global perspective where we are looking at the overall network and the environmental context to see how this shapes the system of connections. Within any social network we have some agent that is choosing to make that connection, agents typically make connections based upon some return on their investment of time energy, interest, social capital or some other resource that they value. An agent makes friends with people whose company they like, they believe in ideologies they value, watch television channels they find interesting, these are all connections that a social actor makes because they value what they get more than what they have to give in making the connection.
There is also the context or environment within which an agent is acting, this environment is exerting some force resisting or enabling them to make a connection, as an example we might think about an oppressive political regime that uses intimidation, coercion and propaganda to prevent people from forming counter political movements, this is a form of resistance, the agents have to overcome their fear in order to make political connections within this environment. This environmental context can be understood as a form of transaction cost, a cost that is being placed on an agent for them to make a connection, inversely it might be a payment where the environment is conducive to them making that connection. This is analogous to an ecosystem where when we turn down the temperature all the creatures hibernate and when we turn it up they come out and interact. The cost of making a connection is not evenly distributed out some options will be easier some more difficult, like water running through some rocks where it finds the course of least resistance.5


Because networks are all about connectivity and processes taking place through those connections, a central and overarching question will be that of network integration.  One of the most important factors with respect to the nature of any society is the question of social cohesion or structural cohesion where we are really asking about the degree of integration to the overall system, as this correlates to such things as social solidarity, shared norms, identity, collective behaviour etc. The idea of social capital is often used as a metric to a society’s degree of cohesion. Social capital may be defined as the network of relationships among people who live and work in a particular society, enabling that society to function effectively.
From this perspective when we ask what is the difference between a socially functional urban community and a socially dysfunctional ghetto, we would say that there is some integration within the first that enables the flow of economic resources and social capital, while we could say the second represents a disintegrated network that inhibits the flow of these resources disconnecting it from the broader social system and rendering it dysfunctional. Of central interest here in how something flows through the whole social network as it is this flow that gives it cohesion. Network integration is a fundamental factor in the makeup of any social system, how integrated the whole system is will be determined by a number of different factors.6


A primary consideration is the density of connections within the whole system, clearly the more connects the more integrated it will be and going from a system with a low level of connectivity to one with a high level represents a very different overall dynamic, at a low level of overall connectivity we are just dealing with a group of people at a high level we actually have a networked system, this fundamentally changes the dynamic.



Clustering is one of the universal features found within social networks where people make connections to others with similar attributes to themselves

A second key consideration affecting the overall integration to a social network is the degree of clustering, clustering is one of the few universal features found in almost all social networks, from the social networks of ancient hunter-gather tribes of Africa to today’s global networks, clustering is derived from the fact that people form connections to people with similar attributes to themselves, what is called homophily and out of this we get global patterns consisting of local communities that have their own distinct structure. These clusters give social networks a distinct heterogeneity to their topology that makes them resistant to the uniform spreading of some phenomena.  

Average Path Length

Another widely encountered phenomena within social networks is that of short average path length, meaning that although a social network may be quite large in terms of its number of members and despite the fact that they may contain significant clustering we often find that any member is connected to any other by just a few links, and this is where we get the famous six degrees of separation hypothesis from. This average path length is again a key metric with respect to the overall integration to the social network. Social solidarity can break down as we scale the community up, the traditional mechanisms for social solidarity that worked for thousands of years as we lived in small rural communities often breaks down in large urban centers. This metric of average path length is very important to social cohesion as it is a primary factor in determining how close everyone will think they are to each other and the degree of interdependence and cohesion.7 

Degree distribution

Another almost universal feature to social networks, is a very high degree of inequality between how connected people are within the network. Here we are talking about degree distribution, a high degree distribution means some people have lots of links while others very few, and we often see that this inequality is quite extreme, in fact it follows a power law distribution, meaning that there will be some who have a very, very high level of connections, such as a celebrity and this is being driven by a positive feedback loop. This degree distribution is again another important determinant to the level of social integration, a low degree distribution gives us a somewhat egalitarian society, with the topology having a certain evenness to it through which the same phenomena can flow to all and this is in contrast to the many socio-cultural systems we see that are in fact highly centralized with significant degrees of inequality in connectivity, that creates some resistance to a uniform spreading.8

Cite this article as: Joss Colchester, "Social Network Analysis," in Complexity Academy, May 3, 2015,

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