Comeparing social networks

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Comeparing social networks

Applying statistical tools to network data Network analysis in the social sciences developed from a conjuncture of anthropologist's observations about relations in face-to-face groups and mathematical graph theory.

A very large part of social network methodology, consequently, deals with relatively small networks, networks where we have confidence in the reliability of our observations about the relations among the actors. Most of the tools of social network analysis involve the use of mathematical functions to describe networks and their sub-structures.

In more recent work, however, some of the focus of social network research has moved away from these roots. Increasingly, the social networks that are being studied may contain many nodes; and, sometimes our observations about these very large networks are based not on censuses, but on samples of nodes.

Network researchers have come to recognize that the relations that they study may be constantly evolving, and that the relations observed at one point in time may not the entirely typical because the pattern of relations is not "in equilibrium.

All of these concerns large networks, sampling, concern about the Comeparing social networks of observations have led social network researchers to begin to apply the techniques of descriptive and inferential statistics in their work.

Statistics provide useful tools for summarizing large amounts of information, and for treating observations as stochastic, rather than deterministic outcomes of social processes.

Descriptive statistics have proven to be of great value because they provide convenient tools to summarize key facts about the distributions of actors, attributes, and relations; statistical tools can describe not only the shape of one distribution, but also joint distributions, or "statistical association.

Inferential statistics have also proven to have very useful applications to social network analysis. At a most general level, the question of "inference" is: Comeparing social networks this chapter we will look at some of the ways in which quite basic statistical tools have been applied in social network analysis.

These are only the starting point. The development of more powerful statistical tools especially tuned for the needs of social network analysis is one of the most rapidly developing "cutting edges" of the field. Many of these tools find immediate application in working with social network data.

There are, however, two quite important distinctive features of applying these tools to network data. First, and most important, social network analysis is about relations among actors, not about relations between variables. Most social scientists have learned their statistics with applications to the study of the distribution of the scores of actors cases on variables, and the relations between these distributions.

Comeparing social networks

We learn about the mean of a set of scores on the variable "income. The application of statistics to social networks is also about describing distributions and relations among distributions. But, rather than describing distributions of attributes of actors or "variables"we are concerned with describing the distributions of relations among actors.

In applying statistics to network data, we are concerned the issues like the average strength of the relations between actors; we are concerned with questions like "is the strength of ties between actors in a network correlated with the centrality of the actors in the network?

Second, many of tools of standard inferential statistics that we learned from the study of the distributions of attributes do not apply directly to network data. Most of the standard formulas for calculating estimated standard errors, computing test statistics, and assessing the probability of null hypotheses that we learned in basic statistics don't work with network data and, if used, can give us "false positive" answers more often than "false negative".

This is because the "observations" or scores in network data are not "independent" samplings from populations. In attribute analysis, it is often very reasonable to assume that Fred's income and Fred's education are a "trial" that is independent of Sue's income and Sue's education. We can treat Fred and Sue as independent replications.

In network analysis, we focus on relations, not attributes. So, one observation might well be Fred's tie with Sue; another observation might be Fred's tie with George; still another might be Sue's tie with George.

These are not "independent" replications. Fred is involved in two observations as are Sue an Georgeit is probably not reasonable to suppose that these relations are "independent" because they both involve George.

The standard formulas for computing standard errors and inferential tests on attributes generally assume independent observations. Applying them when the observations are not independent can be very misleading. Instead, alternative numerical approaches to estimating standard errors for network statistics are used.

These "boot-strapping" and permutations approaches calculate sampling distributions of statistics directly from the observed networks by using random assignment across hundreds or thousands of trials under the assumption that null hypotheses are true. These general points will become clearer as we examine some real cases.

So, let's begin with the simplest univariate descriptive and inferential statistics, and then move on to somewhat more complicated problems. Most of the statistical tools for working with network data can be applied to symmetric data, and data where the relations are valued strength, cost, probability of a tie.

As with any descriptive statistics, the scale of measurement binary or valued does matter in making proper choices about interpretation and application of many statistical tools.

The data that are analyzed with statistical tools when we are working with network data are the observations about relations among actors. If data are symmetric i. What we would like to summarize with our descriptive statistics are some characteristics of the distribution of these scores.

Univariate descriptive statistics for Knoke information and money whole networks For the information sharing relation, we see that we have 90 observations which range from a minimum score of zero to a maximum of one. Since the relation has been coded as a "dummy" variable zero for no relation, one for a relation the mean is also the proportion of possible ties that are present or the densityor the probability that any given tie between two random actors is present Several measures of the variability of the distribution are also given.Competing for In uencers in a Social Network Abstract This paper studies the competition between rms for in uencers in a network.

Firms spend e ort to convince in. The Social Network. Posted on December 20, by Administrator Posted in Computer Science, Python - Advanced, Python Challenges. Six Degrees of Separation The Six degrees of separation is an idea that was originally set out by Frigyes Karinthy in and that can be applied to Social Networks such as Facebook.

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Many of these tools find immediate application in working with social network data.

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There are, however, two quite important distinctive features of applying these tools to network data. First, and most important, social network analysis is about relations among actors, not about relations between variables.

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