networkx.linalg.graphmatrix.incidence_matrix¶

incidence_matrix(G, nodelist=None, edgelist=None, oriented=False, weight=None)[source]

Returns incidence matrix of G.

The incidence matrix assigns each row to a node and each column to an edge. For a standard incidence matrix a 1 appears wherever a row’s node is incident on the column’s edge. For an oriented incidence matrix each edge is assigned an orientation (arbitrarily for undirected and aligning to direction for directed). A -1 appears for the tail of an edge and 1 for the head of the edge. The elements are zero otherwise.

Parameters
• G (graph) – A NetworkX graph

• nodelist (list, optional (default= all nodes in G)) – The rows are ordered according to the nodes in nodelist. If nodelist is None, then the ordering is produced by G.nodes().

• edgelist (list, optional (default= all edges in G)) – The columns are ordered according to the edges in edgelist. If edgelist is None, then the ordering is produced by G.edges().

• oriented (bool, optional (default=False)) – If True, matrix elements are +1 or -1 for the head or tail node respectively of each edge. If False, +1 occurs at both nodes.

• weight (string or None, optional (default=None)) – The edge data key used to provide each value in the matrix. If None, then each edge has weight 1. Edge weights, if used, should be positive so that the orientation can provide the sign.

Returns

A – The incidence matrix of G.

Return type

SciPy sparse matrix

Notes

For MultiGraph/MultiDiGraph, the edges in edgelist should be (u,v,key) 3-tuples.

“Networks are the best discrete model for so many problems in applied mathematics” 1.

References

1

Gil Strang, Network applications: A = incidence matrix, http://academicearth.org/lectures/network-applications-incidence-matrix