Vertex degrees#

Degree functions#

There are multiple ways of defining the degrees for vertices depending on the type of network at hand. All network types have the following degree types defined:

In-degree referes to the number of edges where the vertex is a member of their out-incident set of vertices, i.e., the cardinality of the set of edges that are incoming to that vertex.
Out-degree referes to the number of edges where the vertex is a member of their in-incident set of vertices, i.e., the cardinality of the set of edges that are outgoing from that vertex.
Incident-degree referes to the number of edges where the vertex is a member of their incident set of vertices, i.e., the set of edges that are incoming to or outgoing from that vertex. This should be the sum of in- and out-degree of that vertex.

Python

in_degree(network, vertex) → int#

out_degree(network, vertex) → int#

incident_degree(network, vertex) → int#

C++

template<network_edge EdgeT> std::size_t in_degree(const network<EdgeT> &net, const typename EdgeT::VertexType &vert)#

template<network_edge EdgeT> std::size_t out_degree(const network<EdgeT> &net, const typename EdgeT::VertexType &vert)#

template<network_edge EdgeT> std::size_t incident_degree(const network<EdgeT> &net, const typename EdgeT::VertexType &vert)#

For undirected networks, degree of a vertex referes to the incident-degree of that vertex. For directed networks, the word degree on its own is vaguely-defined.

Python

degree(undirected_network, vertex) → int#

C++

template<undirected_network_edge EdgeT> std::size_t degree(const network<EdgeT> &net, const typename EdgeT::VertexType &vert)#

Degree sequences#

Degree sequence functions return the set of (in-, out- or incident-) degee of vertices in the same order as that of network.vertices(). In- and out-degree pair sequence is a sequence of tuples of in- and out-degrees of vertices.

Python

in_degree_sequence(network) → List[int]#

out_degree_sequence(network) → List[int]#

incident_degree_sequence(network) → List[int]#

in_out_degree_pair_sequence(network) → List[Tuple[int, int]]#

C++

template<network_edge EdgeT> std::vector<std::size_t> in_degree_sequence(const network<EdgeT> &net)#

template<network_edge EdgeT> std::vector<std::size_t> out_degree_sequence(const network<EdgeT> &net)#

template<network_edge EdgeT> std::vector<std::size_t> incident_degree_sequence(const network<EdgeT> &net)#

template<network_edge EdgeT> std::vector<std::pair<std::size_t, std::size_t>> in_out_degree_pair_sequence(const network<EdgeT> &net)#

Similar to degree(), degree sequence without a prefix is only defined for undirected networks.

Python

degree_sequence(undirected_network) → List[int]#

C++

template<undirected_network_edge EdgeT> std::vector<std::size_t> degree_sequence(const network<EdgeT> &net)#