measure_diverse_net: Measures of network diversity
In netrics: Many Ways to Measure and Classify Membership for Networks, Nodes, and Ties
measure_diverse_net R Documentation
Measures of network diversity
Description
These functions offer ways to measure the heterogeneity of an attribute
across a network, within groups of a network, or the distribution of ties
across this attribute:
-
net_by_richness() measures the number of unique categories
in a network attribute.
-
net_by_diversity() measures the heterogeneity of ties across a network.
Usage
net_by_richness(.data, attribute)
net_by_diversity(
.data,
attribute,
diversity = c("blau", "teachman", "variation", "gini")
)
Arguments
.data
A network object of class mnet, igraph, tbl_graph, network, or similar.
For more information on the standard coercion possible,
see manynet::as_tidygraph().
attribute
Name of a nodal attribute, mark, measure, or membership vector.
diversity
Which method to use for *_diversity().
Either "blau" (Blau's index) or "teachman" (Teachman's index) for categorical attributes,
or "variation" (coefficient of variation) or "gini" (Gini coefficient) for numeric attributes.
Default is "blau".
If an incompatible method is chosen for the attribute type,
a suitable alternative will be used instead with a message.
Value
A network_measure numeric score.
Richness
Richness is a simple count of the number of different categories
present for a given attribute.
Diversity
Blau's index (1977) uses a formula known also in other disciplines
by other names
(Gini-Simpson Index, Gini impurity, Gini's diversity index,
Gibbs-Martin index, and probability of interspecific encounter (PIE)):
1 - \sum\limits_{i = 1}^k {p_i^2 }
where p_i is the proportion of group members in ith category
and k is the number of categories for an attribute of interest.
This index can be interpreted as the probability that two members
randomly selected from a group would be from different categories.
This index finds its minimum value (0) when there is no variety,
i.e. when all individuals are classified in the same category.
The maximum value depends on the number of categories and
whether nodes can be evenly distributed across categories.
Teachman's index (1980) is based on information theory
and is calculated as:
- \sum\limits_{i = 1}^k {p_i \log(p_i)}
where p_i is the proportion of group members in ith category
and k is the number of categories for an attribute of interest.
This index finds its minimum value (0) when there is no variety,
i.e. when all individuals are classified in the same category.
The maximum value depends on the number of categories and
whether nodes can be evenly distributed across categories.
It thus shares similar properties to Blau's index,
but includes also a notion of richness that tends to give more weight to
rare categories and thus tends to highlight imbalances more.
The coefficient of variation (CV) is a standardised measure of dispersion
of a probability distribution or frequency distribution.
It is defined as the ratio of the standard deviation \sigma
to the mean \mu:
CV = \frac{\sigma}{\mu}
It is often expressed as a percentage.
The CV is useful because the standard deviation of data must always be understood
in the context of the mean of the data.
The CV is particularly useful when comparing the degree of variation
from one data series to another,
even if the means are drastically different from each other.
The Gini coefficient is a measure of statistical dispersion
that is intended to represent the income or wealth distribution
of a nation's residents,
and is commonly used as a measure of inequality.
It is defined as a ratio with values between 0 and 1,
where 0 corresponds with perfect equality
(everyone has the same income) and 1 corresponds with perfect inequality
(one person has all the income, and everyone else has zero income).
The Gini coefficient can be calculated from the Lorenz curve,
which plots the proportion of the total income of the population
that is cumulatively earned by the bottom x% of the population.
The Gini coefficient is defined as the area between the line of equality
and the Lorenz curve,
divided by the total area under the line of equality.
References
On richness
Magurran, Anne E. 1988.
Ecological Diversity and Its Measurement.
Princeton: Princeton University Press.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-94-015-7358-0")}
On diversity
Blau, Peter M. 1977.
Inequality and heterogeneity.
New York: Free Press.
Teachman, Jay D. 1980.
Analysis of population diversity: Measures of qualitative variation.
Sociological Methods & Research, 8:341-362.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/004912418000800305")}
Page, Scott E. 2010.
Diversity and Complexity.
Princeton: Princeton University Press.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1515/9781400835140")}
See Also
Other diversity:
measure_assort_net,
measure_assort_node,
measure_diverse_node
Other measures:
measure_assort_net,
measure_assort_node,
measure_breadth,
measure_broker_node,
measure_broker_tie,
measure_brokerage,
measure_central_between,
measure_central_close,
measure_central_degree,
measure_central_eigen,
measure_centralities_between,
measure_centralities_close,
measure_centralities_degree,
measure_centralities_eigen,
measure_closure,
measure_closure_node,
measure_cohesion,
measure_core,
measure_diffusion_infection,
measure_diffusion_net,
measure_diffusion_node,
measure_diverse_node,
measure_features,
measure_fragmentation,
measure_hierarchy,
measure_periods
Examples
net_by_richness(ison_networkers)
marvel_friends <- to_unsigned(to_uniplex(fict_marvel, "relationship"), "positive")
net_by_diversity(marvel_friends, "Gender")
net_by_diversity(marvel_friends, "Appearances")
netrics documentation built on July 24, 2026, 5:07 p.m.
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| measure_diverse_net | R Documentation |
Measures of network diversity
Description
These functions offer ways to measure the heterogeneity of an attribute across a network, within groups of a network, or the distribution of ties across this attribute:
-
net_by_richness()measures the number of unique categories in a network attribute. -
net_by_diversity()measures the heterogeneity of ties across a network.
Usage
net_by_richness(.data, attribute)
net_by_diversity(
.data,
attribute,
diversity = c("blau", "teachman", "variation", "gini")
)
Arguments
.data |
A network object of class |
attribute |
Name of a nodal attribute, mark, measure, or membership vector. |
diversity |
Which method to use for |
Value
A network_measure numeric score.
Richness
Richness is a simple count of the number of different categories present for a given attribute.
Diversity
Blau's index (1977) uses a formula known also in other disciplines by other names (Gini-Simpson Index, Gini impurity, Gini's diversity index, Gibbs-Martin index, and probability of interspecific encounter (PIE)):
1 - \sum\limits_{i = 1}^k {p_i^2 }
where p_i is the proportion of group members in ith category
and k is the number of categories for an attribute of interest.
This index can be interpreted as the probability that two members
randomly selected from a group would be from different categories.
This index finds its minimum value (0) when there is no variety,
i.e. when all individuals are classified in the same category.
The maximum value depends on the number of categories and
whether nodes can be evenly distributed across categories.
Teachman's index (1980) is based on information theory and is calculated as:
- \sum\limits_{i = 1}^k {p_i \log(p_i)}
where p_i is the proportion of group members in ith category
and k is the number of categories for an attribute of interest.
This index finds its minimum value (0) when there is no variety,
i.e. when all individuals are classified in the same category.
The maximum value depends on the number of categories and
whether nodes can be evenly distributed across categories.
It thus shares similar properties to Blau's index,
but includes also a notion of richness that tends to give more weight to
rare categories and thus tends to highlight imbalances more.
The coefficient of variation (CV) is a standardised measure of dispersion
of a probability distribution or frequency distribution.
It is defined as the ratio of the standard deviation \sigma
to the mean \mu:
CV = \frac{\sigma}{\mu}
It is often expressed as a percentage. The CV is useful because the standard deviation of data must always be understood in the context of the mean of the data. The CV is particularly useful when comparing the degree of variation from one data series to another, even if the means are drastically different from each other.
The Gini coefficient is a measure of statistical dispersion that is intended to represent the income or wealth distribution of a nation's residents, and is commonly used as a measure of inequality. It is defined as a ratio with values between 0 and 1, where 0 corresponds with perfect equality (everyone has the same income) and 1 corresponds with perfect inequality (one person has all the income, and everyone else has zero income). The Gini coefficient can be calculated from the Lorenz curve, which plots the proportion of the total income of the population that is cumulatively earned by the bottom x% of the population. The Gini coefficient is defined as the area between the line of equality and the Lorenz curve, divided by the total area under the line of equality.
References
On richness
Magurran, Anne E. 1988. Ecological Diversity and Its Measurement. Princeton: Princeton University Press. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-94-015-7358-0")}
On diversity
Blau, Peter M. 1977. Inequality and heterogeneity. New York: Free Press.
Teachman, Jay D. 1980. Analysis of population diversity: Measures of qualitative variation. Sociological Methods & Research, 8:341-362. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/004912418000800305")}
Page, Scott E. 2010. Diversity and Complexity. Princeton: Princeton University Press. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1515/9781400835140")}
See Also
Other diversity:
measure_assort_net,
measure_assort_node,
measure_diverse_node
Other measures:
measure_assort_net,
measure_assort_node,
measure_breadth,
measure_broker_node,
measure_broker_tie,
measure_brokerage,
measure_central_between,
measure_central_close,
measure_central_degree,
measure_central_eigen,
measure_centralities_between,
measure_centralities_close,
measure_centralities_degree,
measure_centralities_eigen,
measure_closure,
measure_closure_node,
measure_cohesion,
measure_core,
measure_diffusion_infection,
measure_diffusion_net,
measure_diffusion_node,
measure_diverse_node,
measure_features,
measure_fragmentation,
measure_hierarchy,
measure_periods
Examples
net_by_richness(ison_networkers)
marvel_friends <- to_unsigned(to_uniplex(fict_marvel, "relationship"), "positive")
net_by_diversity(marvel_friends, "Gender")
net_by_diversity(marvel_friends, "Appearances")
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