# NetworkX 1.6#

Release date: 20 November 2011

## Highlights#

New functions for finding articulation points, generating random bipartite graphs, constructing adjacency matrix representations, forming graph products, computing assortativity coefficients, measuring subgraph centrality and communicability, finding k-clique communities, and writing JSON format output.

New examples for drawing with D3 JavaScript library, and ordering matrices with the Cuthill-McKee algorithm.

More memory efficient implementation of current-flow betweenness and new approximation algorithms for current-flow betweenness and shortest-path betweenness.

Simplified handling of “weight” attributes for algorithms that use weights/costs/values.

Updated all code to work with the PyPy Python implementation http://pypy.org which produces faster performance on many algorithms.

### Graph Classes#

The degree* methods in the graph classes (Graph, DiGraph, MultiGraph, MultiDiGraph) now take an optional weight= keyword that allows computing weighted degree with arbitrary (numerical) edge attributes. Setting weight=None is equivalent to the previous weighted=False.

### Weighted graph algorithms#

Many ‘weighted’ graph algorithms now take optional parameter to specify which edge attribute should be used for the weight (default=’weight’) (ticket https://networkx.lanl.gov/trac/ticket/573)

In some cases the parameter name was changed from weighted, to weight. Here is how to specify which edge attribute will be used in the algorithms:

• Use weight=None to consider all weights equally (unweighted case)

• Use weight=’weight’ to use the ‘weight’ edge attribute

• Use weight=’other’ to use the ‘other’ edge attribute

Algorithms affected are:

to_scipy_sparse_matrix, clustering, average_clustering, bipartite.degree, spectral_layout, neighbor_degree, is_isomorphic, betweenness_centrality, betweenness_centrality_subset, vitality, load_centrality, mincost, shortest_path, shortest_path_length, average_shortest_path_length

### Isomorphisms#

Node and edge attributes are now more easily incorporated into isomorphism checks via the ‘node_match’ and ‘edge_match’ parameters. As part of this change, the following classes were removed:

```WeightedGraphMatcher
WeightedDiGraphMatcher
WeightedMultiGraphMatcher
WeightedMultiDiGraphMatcher
```

The function signature for ‘is_isomorphic’ is now simply:

```is_isomorphic(g1, g2, node_match=None, edge_match=None)
```

See its docstring for more details. To aid in the creation of ‘node_match’ and ‘edge_match’ functions, users are encouraged to work with:

```categorical_node_match
categorical_edge_match
categorical_multiedge_match
numerical_node_match
numerical_edge_match
numerical_multiedge_match
generic_node_match
generic_edge_match
generic_multiedge_match
```

These functions construct functions which can be passed to ‘is_isomorphic’. Finally, note that the above functions are not imported into the top-level namespace and should be accessed from ‘networkx.algorithms.isomorphism’. A useful import statement that will be repeated throughout documentation is:

```import networkx.algorithms.isomorphism as iso
```

### Other#

• attracting_components

A list of lists is returned instead of a list of tuples.

• condensation

The condensation algorithm now takes a second argument (scc) and returns a graph with nodes labeled as integers instead of node tuples.

• degree connectivity

average_in_degree_connectivity and average_out_degree_connectivity have been replaced with

average_degree_connectivity(G, source=’in’, target=’in’)

and

average_degree_connectivity(G, source=’out’, target=’out’)

• neighbor degree

average_neighbor_in_degree and average_neighbor_out_degreey have have been replaced with

average_neighbor_degree(G, source=’in’, target=’in’)

and

average_neighbor_degree(G, source=’out’, target=’out’)