Edge degrees (orders)#

Degree functions#

There are multiple ways of defining the degrees for (hyper-)edges depending on the type of edge. All edge types have the following degree functions defined:

Edge in-degree referes to the number of vertices that are in-incident to the edge, i.e., the cardinality of the set of mutator vertices of the edge.
Edge out-degree referes to the number of vertices that are out-incident to the edge, i.e., the cardinality of the set of mutated vertices of the edge.
Edge incident-degree referes to the number of vertices incident to the edge.

Note

Unlike vertex degrees, edge degree functions do not require a network to be passed as the first argument. This is because the degree of an edge can be determined by the edge itself.

Python

edge_in_degree(edge) → int#

edge_out_degree(edge) → int#

edge_incident_degree(edge) → int#

C++

template<network_edge EdgeT> std::size_t edge_in_degree(const EdgeT &edge)#

template<network_edge EdgeT> std::size_t edge_out_degree(const EdgeT &edge)#

template<network_edge EdgeT> std::size_t edge_incident_degree(const EdgeT &edge)#

For undirected edges, degree of a edge referes to the incident-degree of that edge. For directed edges, the word degree on its own is vaguely-defined. In hypergraphs, this is commonly refered to as the order of the edge.

Python

edge_degree(edge) → int#

C++

template<undirected_network_edge EdgeT> std::size_t edge_degree(const EdgeT &edge)#

Edge degree sequences#

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

Python

edge_in_degree_sequence(network) → List[int]#

edge_out_degree_sequence(network) → List[int]#

edge_incident_degree_sequence(network) → List[int]#

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

C++

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

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

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

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

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

Python

edge_degree_sequence(undirected_network) → List[int]#

C++

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