Assortativity

Note

The methods in this section rely on calculating the Pearson correlation coefficient between pairs of value sequences. If the network is regular (i.e. all vertices have equal degree or label) or if the network has fewer than two pairs of interacting vertices, the result of calculating assortativity will be NaN.

Degree assortativity

Undirected networks

Python

degree_assortativity(undirected_network) → float

C++

template<undirected_static_network_edge EdgeT>
double degree_assortativity(const network<EdgeT> &net)

Calculates degree assortativity for undirected dyadic and hypergraph static networks. Assortativity is calculated through Pearson correlation coefficient over degrees of all pairs of interacting vertices.

Directed networks

Python

in_in_degree_assortativity(directed_network) → float

in_out_degree_assortativity(directed_network) → float

out_in_degree_assortativity(directed_network) → float

out_out_degree_assortativity(directed_network) → float

C++

template<directed_static_network_edge EdgeT>
double in_in_degree_assortativity(const network<EdgeT> &net)

template<directed_static_network_edge EdgeT>
double in_out_degree_assortativity(const network<EdgeT> &net)

template<directed_static_network_edge EdgeT>
double out_in_degree_assortativity(const network<EdgeT> &net)

template<directed_static_network_edge EdgeT>
double out_out_degree_assortativity(const network<EdgeT> &net)

Calculates in-/out-degree assortativity for directed dyadic and hypergraph static networks. Assortativity is calculated through Pearson correlation coefficient over degrees of all pairs of interacting vertices.

Numerical attribute assortativity

Undirected networks

Python

attribute_assortativity(undirected_network, attribute_fun: Callable[[network.edge_type()], float]) → float

C++

template<undirected_static_network_edge EdgeT, std::invocable<const typename EdgeT::VertexType&> AttrFun>
requires std::convertible_to<std::invoke_result_t<AttrFun, const typename EdgeT::VertexType&>, double>
double attribute_assortativity(const network<EdgeT> &net, AttrFun &&attribute_fun)

Calculates assortativity of the given numerical function for undirected dyadic and hypergraph static networks. Assortativity is calculated through Pearson correlation coefficient over the value of the given function over all pairs of interacting vertices.

Python

attribute_assortativity(undirected_network, attribute_map: dict[network.edge_type(), float], default_value: float) → float

C++

template<network_edge EdgeT, mapping<EdgeT, double> MapT>
double attribute_assortativity(const network<EdgeT> &net, const MapT &attribute_map, double default_value)

Calculates assortativity of the given mapping of vertices to floating-point (dictionary) for undirected dyadic and hypergraph static networks. Assortativity is calculated through Pearson correlation coefficient over the value of the given mapping over all pairs of interacting vertices. If a vertex is not present in the mapping, the value of the argument default_value is used.

Directed networks

Python

attribute_assortativity(directed_network, mutator_attribute_fun: Callable[[network.edge_type()], float], mutated_attribute_fun: Callable[[network.edge_type()], float]) → float

C++

template<undirected_static_network_edge EdgeT, std::invocable<const typename EdgeT::VertexType&> AttrFun1, std::invocable<const typename EdgeT::VertexType&> AttrFun2>
requires std::convertible_to<std::invoke_result_t<AttrFun1, const typename EdgeT::VertexType&>, double> && std::convertible_to<std::invoke_result_t<AttrFun2, const typename EdgeT::VertexType&>, double>
double attribute_assortativity(const network<EdgeT> &net, AttrFun1 &&mutator_attribute_fun, AttrFun2 &&mutated_attribute_fun)

Calculates assortativity of the given numerical functions for directed dyadic and hypergraph static networks. Assortativity is calculated through Pearson correlation coefficient over the value of the given function over all pairs of interacting vertices. The associated value of the mutator (tail of the arrow representation of a directed link) is calculated from the function mutator_attribute_fun, and the mutated vertex (head of the arrow) from mutated_attribute_fun.

Python

attribute_assortativity(directed_network, mutator_attribute_map: dict[network.edge_type(), float], mutated_attribute_map: dict[network.edge_type(), float], mutator_default_value: float, mutated_default_value: float) → float

C++

template<network_edge EdgeT, mapping<EdgeT, double> MapT1, mapping<EdgeT, double> MapT2>
double attribute_assortativity(const network<EdgeT> &net, const MapT1 &mutator_attribute_map, const MapT2 &mutated_attribute_map, double mutator_default_value, double mutated_default_value)

Calculates assortativity of the given pair of mappings of vertices to floating-point (dictionaries) for directed dyadic and hypergraph static networks. Assortativity is calculated through Pearson correlation coefficient over the value of the given pair of mappings over all pairs of interacting vertices. If a vertex is not present in one of the mappings, the value of the argument mutator_default_value or mutated_attribute_fun is used. The associated value of the mutator (tail of the arrow representation of a directed link) is calculated from the function mutator_attribute_fun, and the mutated vertex (head of the arrow) from mutated_attribute_fun.