# Social Structure And Network (A Mathematical Model For Social Behaviour)

Analogy and metaphor are often used by social scientists to explain a social phenomenon because certain social concepts are otherwise very difficult to comprehend. For example, a physical structure like ‘building’ or a biological structure like ‘organism’ is compared to define the concept ‘social structure’. Actually, social structure is not a physical structure. An abstract concept which can’t be seen is explained in a simplified way by using an analogy which can be seen easily by everyone. Physical scientists use a model to test the predictions. If the predictions are correct when the model is tested every time then the model constructed is perfect. Otherwise, the model is suitably modified and then the predictions are tested again. This process is continued until the model becomes perfect. Do we have a grand model of social structure that can be used to test social predictions? In this article, an attempt is made to understand how far network theory is useful in explaining social structure and whether social predictions can be made using the network.

Radcliffe-Brown was one of the earliest to recognise that the analysis of social structure would ultimately take a mathematical form. Radcliffe-Brown defines social structure as a ‘set of actually existing relations at a given moment of time, which link together certain human beings’. According to Oxford dictionary, ‘relations’ means the way in which two persons, groups, or countries behave towards each other or deal with each other. The phrase, ‘link together certain human beings’ can be compared with a ‘net work’ of connections.

Network is defined as a closely connected group of people who exchange information. Each point (person or agent) in the network is called a ‘node’ and the link between two nodes is connected by a line called an ‘edge’. When two nodes have a direct social relation then they are connected with an edge. So when a node is connected with all possible nodes with which the node has social relations, it produces a graph. The resulting graph is a social network. The number of edges in a network is given by a formula nc2, where ‘n’ is the number of nodes. For example, if there are 3 people in a party then the number of handshakes will be 3. If there are 4 people then the number of handshakes will be 6. If there are 5 people then it will be 10. If there are 10 people then the number of handshakes will be 45. If there are 1000 people then the number of handshakes will be 499,500. When the number of people has increased 100 folds from 10 to 1000, the number of handshakes has increased 10,000 folds. So the number of relationships increases significantly as ‘n’ increases. The network theory was developed by the Hungarian mathematicians, Paul Erdos and Alfred Renyi, in the mid twentieth-century. Networks of nodes that can be in a state of 0 or 1 are called Boolean networks. It was invented by the mathematician George Boole. In Boolean networks, the 0 or 1 state of the nodes is determined by a set of rules.

If two nodes are connected then the network of the two nodes assumes four states (00, 01, 10, and 11). The number of states of network grows exponentially as the number of nodes netvigator 優惠 increases which is obtained by a formula 2n, where ‘n’ is the number of nodes. When n is greater than 100, it is quite difficult to explore all the possible states of the network even for the world’s fastest computer. In a Boolean network we can fix the number of states as 0 and 1. In a Boolean network, if there are three nodes A, B, and C which are connected directly by edges then the state of C can be determined by fixing the states of A and B. It means the state of C depends upon the states of A and B in some combination. Further it implies that if we know the state of C then we will know the combinational behaviour of A and B. But in a social network of persons, we do not know how a person’s behaviour is deterministic. Further, in a Boolean network, the behaviour of the nodes can be studied in controlled experiments as nodes here are objects. But in a social network, nodes which are individual persons can’t be treated as objects. In a social network how do we define the states of a person? How many states does a person have? What is the nature of a state? If the expected behaviour of a person is reduced to two states like ‘yes’ or ‘no’, then the number of states of a network will be 2n. Out of this, only one state will show up at a given moment of time. How do we predict that one particular state?

Family is a micro network within the network. The family members are closely connected with each other. Most of the members are also connected to other networks external to the family. Interactions take place within the family among the members who also have interactions outside the family. So there are several edges proceed from one node of a family towards nodes within the family and nodes outside the family. The edges within a family show intimate relationship, whereas the edges connecting nodes outside the family do not necessarily show intimate relationship. This intimate relationship is a very important assumption that we have to consider so as to reduce the number of states of the social network. For example, the likelihood of a family member to conform to the family norms will be higher. Similarly, the likelihood of a person to side with a close friend will be higher. Also, the likelihood of a member of a particular group to conform to group norms will be higher. These assumptions are necessary to measure the probability of how the whole network behaves in a certain way.