# Modeling Network Dynamics: Random Networks

DOI: 10.4018/978-1-7998-1912-7.ch008
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## Abstract

Social relationships and the social networks over these relationships do not occur arbitrarily. However, the random networks dealt with in this chapter are important tools for modeling the networks of these systems. The authors use random networks to understand and to model dynamics regarding the whole social structure. Random network models became the topic of several studies independently from social network analysis in the 1950s. These models were used in the analysis of a wide range of social and non-social phenomena, from electrical and communication networks to the speed and manner of disease propagation. This chapter explores the modeling network dynamics of random networks.
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`hist(trees\$Height,breaks=)`
Figure 1.

A normal distribution

```summary(trees\$Height)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
##      63      72      76      76      80      87```

Similar to the example, we use random networks to understand and to model dynamics regarding the whole social structure. In one of the first examples of modeling effort, Moreno and Jennings developed graph-based estimations in order to show that reciprocity in relationships is not arbitrary and that it is a dominant type of social behavior (Moreno and Jennings 1938). In other words they have calculated how much more reciprocity was actually there in a network compared to the baseline of ties (and hence reciprocating ties) being entirely random. Such a way of estimation allows us to indicate whether there is a different kind of reciprocity behavior in a certain social network when compared with others.

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## Basic Modeling Concepts And Early Studies On Random Models

Let us name the data collected for a social network as “observed network”. In random network modeling, this network is the occurrence of a random event in a probability space (we can say that we are dealing with a non- Bayesian branch of probability). Random network modeling assumes that we know some characteristics of the network (for example, and especially, the number of actors), but we do not know how the network pattern is generated randomly. The purpose of the modeling is to create and test hypotheses concerning this random process (Robins et al. 2007). A variety of models were proposed in the literature.

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