population density
The average number of people who live on each square mile (or kilometer) of land.
Examples of population density in the following topics:

U.S. Urban Patterns
 Census Bureau classifies areas as urban or rural based on population size and density.
 Usually, this type of population center is associated with a cluster of industrial and cultural enterprises.
 Other definitions may consider total population size or population density.
 The Census Bureau defines "urban areas" as areas with a population density of at least 1,000 people per square mile and at least 2,500 total people.
 For example, the city of Greenville, South Carolina has a city population under 60,000 and an urbanized area population of over 300,000, while Greensboro, North Carolina has a city population over 200,000 and an urbanized area population of around 270,000.

Density
 If we are comparing two populations, and we note that there are many actors in one that are not connected to any other ("isolates"), and in the other population most actors are embedded in at least one dyad  we would likely conclude that social life is very different in the two populations.
 Measuring the density of a network gives us a ready index of the degree of dyadic connection in a population.
 Network>Cohesion>Density is a useful tool for calculating the density of whole populations, or of partitions.
 We can see that the three subpopulations appear to have some differences.
 Governmental generalists (block 1) have quite dense in and out ties to one another, and to the other populations; nongovernment generalists (block 2) have outties among themselves and with block 1, and have high densities of inties with all three subpopulations.

Summary
 There is a great deal of information about both individuals and the population in a single adjacency matrix.
 In this chapter you have learned a lot of terminology for describing the connections and distances between actors, and for whole populations.
 The local connections of actors are important for understanding the social behavior of the whole population, as well as for understanding each individual.
 The size of the network, its density, whether all actors are reachable by all others (i.e. is the whole population connected, or are there multiple components?
 Populations with high density respond differently to challenges from the environment than those with low density; populations with greater diversity in individual densities may be more likely to develop stable social differentiation and stratification.

Clustering
 The "weighted" version gives weight to the neighborhood densities proportional to their size; that is, actors with larger neighborhoods get more weight in computing the average density.
 Lest we overinterpret, we must remember that the overall density of the entire graph in this population is rather high (.54).
 So, the density of local neighborhoods is not really much higher than the density of the whole graph.
 In assessing the degree of clustering, it is usually wise to compare the cluster coefficient to the overall density.
 We can also examine the densities of the neighborhoods of each actor, as is shown in figure 8.9.

Hypotheses about one mean or density
 We may want to test hypotheses about the density or mean tie strength of a network.
 Network>Compare densities>Against theoretical parameter performs a statistical test to compare the value of a density or average tie strength observed in a network against a test value.
 But, perhaps the difference between what we see (density = .544) and what the theory predicts (density = 1.000) is due to random variation (perhaps when we collected the information).
 The "Expected density" is the value against which we want to test.
 How often would a difference this large happen by random sampling variation, if the null hypothesis (density = 1.000) was really true in the population?

Density
 The density of a binary network is simply the proportion of all possible ties that are actually present.
 Network>Cohesion>Density is a quite powerful tool for calculating densities.
 The Network>Cohesion>Density algorithm also can be used to calculate the densities within partitions or blocks by specifying the file name of an attribute data set that contains the node name and partition number.
 That is, the density tool can be used to calculate within and between block densities for data that are grouped.
 Or, it may indicate that the population we are studying is really composed of more than one subpopulations.

Study Questions
 Why is population size so important is sociological analysis?
 How is density measured?
 Why is density important is sociological analysis?
 Which studies used the ideas of connectedness and density?
 What is the density of the ties?

Population Trends
 Despite an overall pattern of growth, population trends are not even across countries.
 Overpopulation is not a function of the number or density of the individuals, but rather the number of individuals compared to the resources they need to survive.
 About half the world population lives in nations with subreplacement fertility.
 Presently, the world's population grows by approximately 80 million annually.
 Once the population exceeded the planet's carrying capacity, the population would be restrained through mass famine and starvation.

Factions
 Imagine a society in which each person was closely tied to all others in their own subpopulation (that is, all subpopulations are cliques), and there are no connections at all among subpopulations (that is, each subpopulation is a component).
 Most real populations do not look like this, but the "ideal type" of complete connection within and complete disconnection between subgroups is a useful reference point for assessing the degree of "factionalization" in a population.
 We can see that there is quite a lot of density "off the main diagonal" where there shouldn't be any.
 The final panel of the results reports the "block densities" as the number of ties that are present in blocks as proportions of all possible ties.
 This approach corresponds nicely to the intuitive notion that the groups of a graph can be defined by a combination of local high density, and the presence of "structural holes" between some sets of actors and others.

Groupexternal and groupinternal ties
 The EI index can be applied at three levels: the entire population, each group, and each individual.
 That is, the network as a whole (all the groups) can be characterized in terms of the boundedness and closure of its subpopulations.
 The observed block densities are presented first.
 Since any tie (in or out) is regarded as a tie, the densities in this example are quite high.
 The densities off the main diagonal (outgroup ties) appear to be slightly more prevalent than the densities on the main diagonal (ingroup ties).