infomap module

class infomap.Infomap(args=None, cluster_data=None, no_infomap=False, skip_adjust_bipartite_flow=False, bipartite_teleportation=False, weight_threshold=None, include_self_links=None, no_self_links=False, node_limit=None, matchable_multilayer_ids=None, assign_to_neighbouring_module=False, meta_data=None, meta_data_rate=1.0, meta_data_unweighted=False, tree=False, ftree=False, clu=False, verbosity_level=1, silent=False, out_name=None, no_file_output=False, clu_level=None, output=None, hide_bipartite_nodes=False, print_all_trials=False, two_level=False, flow_model=None, directed=None, recorded_teleportation=False, use_node_weights_as_flow=False, to_nodes=False, teleportation_probability=0.15, regularized=False, regularization_strength=1.0, entropy_corrected=False, entropy_correction_strength=1.0, markov_time=1.0, variable_markov_time=False, variable_markov_damping=1.0, preferred_number_of_modules=None, multilayer_relax_rate=0.15, multilayer_relax_limit=-1, multilayer_relax_limit_up=-1, multilayer_relax_limit_down=-1, multilayer_relax_by_jsd=False, seed=123, num_trials=1, core_loop_limit=10, core_level_limit=None, tune_iteration_limit=None, core_loop_codelength_threshold=1e-10, tune_iteration_relative_threshold=1e-05, fast_hierarchical_solution=None, prefer_modular_solution=False, inner_parallelization=False)

Bases: InfomapWrapper

This class is a thin wrapper around Infomap C++ compiled with SWIG.

Examples

Create an instance and add nodes and links:

>>> from infomap import Infomap
>>> im = Infomap(silent=True)
>>> im.add_node(1)
>>> im.add_node(2)
>>> im.add_link(1, 2)
>>> im.run()
>>> im.codelength
1.0

Create an instance and read a network file:

>>> from infomap import Infomap
>>> im = Infomap(silent=True, num_trials=10)
>>> im.read_file("ninetriangles.net")
>>> im.run()
>>> tol = 1e-4
>>> abs(im.codelength - 3.4622731375264144) < tol
True

For more examples, see the examples directory.

__init__(args=None, cluster_data=None, no_infomap=False, skip_adjust_bipartite_flow=False, bipartite_teleportation=False, weight_threshold=None, include_self_links=None, no_self_links=False, node_limit=None, matchable_multilayer_ids=None, assign_to_neighbouring_module=False, meta_data=None, meta_data_rate=1.0, meta_data_unweighted=False, tree=False, ftree=False, clu=False, verbosity_level=1, silent=False, out_name=None, no_file_output=False, clu_level=None, output=None, hide_bipartite_nodes=False, print_all_trials=False, two_level=False, flow_model=None, directed=None, recorded_teleportation=False, use_node_weights_as_flow=False, to_nodes=False, teleportation_probability=0.15, regularized=False, regularization_strength=1.0, entropy_corrected=False, entropy_correction_strength=1.0, markov_time=1.0, variable_markov_time=False, variable_markov_damping=1.0, preferred_number_of_modules=None, multilayer_relax_rate=0.15, multilayer_relax_limit=-1, multilayer_relax_limit_up=-1, multilayer_relax_limit_down=-1, multilayer_relax_by_jsd=False, seed=123, num_trials=1, core_loop_limit=10, core_level_limit=None, tune_iteration_limit=None, core_loop_codelength_threshold=1e-10, tune_iteration_relative_threshold=1e-05, fast_hierarchical_solution=None, prefer_modular_solution=False, inner_parallelization=False)

Create a new Infomap instance.

Parameters:
  • args (str, optional) – String of Infomap arguments.

  • cluster_data (str, optional) – Provide an initial two-level (clu format) or multi-layer (tree format) solution.

  • no_infomap (bool, optional) – Don’t run the optimizer. Useful to calculate codelength of provided cluster data or to print non-modular statistics.

  • skip_adjust_bipartite_flow (bool, optional) – Skip distributing all flow from the bipartite nodes to the primary nodes.

  • bipartite_teleportation (bool, optional) – Teleport like the bipartite flow instead of two-step (unipartite) teleportation.

  • weight_threshold (float, optional) – Limit the number of links to read from the network. Ignore links with less weight than the threshold.

  • include_self_links (bool, optional) – Include links with the same source and target node. DEPRECATED. Include self links by default now, exclude with no_self_links.

  • no_self_links (bool, optional) – Exclude self links in the input network.

  • node_limit (int, optional) – Limit the number of nodes to read from the network. Ignore links connected to ignored nodes.

  • matchable_multilayer_ids (int, optional) – Construct state ids from node and layer ids that are consistent across networks for the same max number of layers. Set to at least the largest layer id among networks to match.

  • assign_to_neighbouring_module (bool, optional) – Assign nodes without module assignments (from cluster_data) to the module assignment of a neighbouring node if possible.

  • meta_data (str, optional) – Provide meta data (clu format) that should be encoded.

  • meta_data_rate (float, optional) – Metadata encoding rate. Default is to encode each step.

  • meta_data_unweighted (bool, optional) – Don’t weight meta data by node flow.

  • tree (bool, optional) – Write a tree file with the modular hierarchy. Automatically enabled if no other output is specified.

  • ftree (bool, optional) – Write a ftree file with the modular hierarchy including aggregated links between (nested) modules.

  • clu (bool, optional) – Write a clu file with the top cluster ids for each node.

  • verbosity_level (int, optional) – Verbose output on the console.

  • silent (bool, optional) – No output on the console.

  • out_name (str, optional) – Name for the output files, e.g. "[output_directory]/[out-name].tree"

  • no_file_output (bool, optional) – Don’t write output to file.

  • clu_level (int, optional) – For clu output, print modules at specified depth from root. Use -1 for bottom level modules.

  • output (list(str), optional) – List of output formats. Options: clu, tree, ftree, newick, json, csv, network, states.

  • hide_bipartite_nodes (bool, optional) – Project bipartite solution to unipartite.

  • print_all_trials (bool, optional) – Print all trials to separate files.

  • two_level (bool, optional) – Optimize a two-level partition of the network. Default (false) is multi-level.

  • flow_model (str, optional) – Specify flow model. Options: undirected, directed, undirdir, outdirdir, rawdir.

  • directed (bool, optional) – Assume directed links. Shorthand for flow_model="directed".

  • recorded_teleportation (bool, optional) – If teleportation is used to calculate the flow, also record it when minimizing codelength. Default False.

  • use_node_weights_as_flow (bool, optional) – Use node weights (from api or after names in Pajek format) as flow, normalized to sum to 1.

  • to_nodes (bool, optional) – Teleport to nodes instead of to links, assuming uniform node weights if no such input data.

  • teleportation_probability (float, optional) – Probability of teleporting to a random node or link.

  • regularized (bool, optional) – Effectively add a fully connected Bayesian prior network to not overfit due to missing links. Implies recorded teleportation.

  • regularization_strength (float, optional) – Adjust relative strength of Bayesian prior network with this multiplier.

  • entropy_corrected (bool, optional) – Correct for negative entropy bias in small samples (many modules).

  • entropy_correction_strength (float, optional) – Increase or decrease the default entropy correction with this multiplier.

  • markov_time (float, optional) – Scales link flow to change the cost of moving between modules. Higher values results in fewer modules.

  • variable_markov_time (bool, optional) – Increase Markov time locally to level out link flow. Reduces risk of overpartitioning sparse areas while keeping high resolution in dense areas.

  • variable_markov_damping (float, optional) – Damping parameter for variable Markov time, to scale with local effective degree (0) or local entropy (1).

  • preferred_number_of_modules (int, optional) – Penalize solutions the more they differ from this number.

  • multilayer_relax_rate (float, optional) – Probability to relax the constraint to move only in the current layer.

  • multilayer_relax_limit (int, optional) – Number of neighboring layers in each direction to relax to. If negative, relax to any layer.

  • multilayer_relax_limit_up (int, optional) – Number of neighboring layers with higher id to relax to. If negative, relax to any layer.

  • multilayer_relax_limit_down (int, optional) – Number of neighboring layers with lower id to relax to. If negative, relax to any layer.

  • multilayer_relax_by_jsd (bool, optional) – Relax proportional to the out-link similarity measured by the Jensen-Shannon divergence.

  • seed (int, optional) – A seed (integer) to the random number generator for reproducible results.

  • num_trials (int, optional) – Number of outer-most loops to run before picking the best solution.

  • core_loop_limit (int, optional) – Limit the number of loops that tries to move each node into the best possible module.

  • core_level_limit (int, optional) – Limit the number of times the core loops are reapplied on existing modular network to search bigger structures.

  • tune_iteration_limit (int, optional) – Limit the number of main iterations in the two-level partition algorithm. 0 means no limit.

  • core_loop_codelength_threshold (float, optional) – Minimum codelength threshold for accepting a new solution in core loop.

  • tune_iteration_relative_threshold (float, optional) – Set codelength improvement threshold of each new tune iteration to f times the initial two-level codelength.

  • fast_hierarchical_solution (int, optional) – Find top modules fast. Use 2 to keep all fast levels. Use 3 to skip recursive part.

  • prefer_modular_solution (bool, optional) – Prefer modular solutions even if they are worse than putting all nodes in one module.

  • inner_parallelization (bool, optional) – Parallelize the inner-most loop for greater speed. This may give some accuracy tradeoff.

Add a link.

Notes

If the source or target nodes does not exist, they will be created.

See also

remove_link

Parameters:
  • source_id (int) –

  • target_id (int) –

  • weight (float, optional) –

Add several links.

Examples

>>> from infomap import Infomap
>>> im = Infomap()
>>> links = (
...     (1, 2),
...     (1, 3)
... )
>>> im.add_links(links)

See also

add_link, remove_link

Parameters:

links (iterable of tuples) – Iterable of tuples of int of the form (source_id, target_id, [weight])

Add an inter-layer link.

Adds a link between two layers in a multilayer network. The link is specified through a shared physical node, but that jump will not be recorded so Infomap will spread out this link to the next possible steps for the random walker in the target layer.

Notes

This multilayer format requires a directed network, so if the directed flag is not present, it will add all links also in their opposite direction to transform the undirected input to directed. If no inter-layer links are added, Infomap will simulate these by relaxing the random walker’s constraint to its current layer. The final state network will be generated on run, which will clear the temporary data structure that holds the provided inter-layer links.

Examples

>>> from infomap import Infomap
>>> im = Infomap()
>>> im.add_multilayer_inter_link(1, 1, 2)
>>> im.add_multilayer_inter_link(1, 2, 2)
>>> im.add_multilayer_inter_link(2, 1, 1)
>>> im.add_multilayer_inter_link(2, 3, 1)
Parameters:
  • source_layer_id (int) –

  • node_id (int) –

  • target_layer_id (int) –

  • weight (float, optional) –

Add an intra-layer link.

Adds a link within a layer in a multilayer network.

Examples

>>> from infomap import Infomap
>>> im = Infomap()
>>> im.add_multilayer_intra_link(1, 1, 2)
>>> im.add_multilayer_intra_link(1, 2, 3)
>>> im.add_multilayer_intra_link(2, 1, 3)
>>> im.add_multilayer_intra_link(2, 3, 4)

Notes

This multilayer format requires a directed network, so if the directed flag is not present, it will add all links also in their opposite direction to transform the undirected input to directed. If no inter-layer links are added, Infomap will simulate those by relaxing the random walker’s constraint to its current layer. The final state network will be generated on run, which will clear the temporary data structure that holds the provided intra-layer links.

Parameters:
  • layer_id (int) –

  • source_node_id (int) –

  • target_node_id (int) –

  • weight (float, optional) –

Add a multilayer link.

Adds a link between layers in a multilayer network.

Examples

Usage with tuples:

>>> from infomap import Infomap
>>> im = Infomap()
>>> source_multilayer_node = (0, 1) # layer_id, node_id
>>> target_multilayer_node = (1, 2) # layer_id, node_id
>>> im.add_multilayer_link(source_multilayer_node, target_multilayer_node)

Usage with MultilayerNode

>>> from infomap import Infomap, MultilayerNode
>>> im = Infomap()
>>> source_multilayer_node = MultilayerNode(layer_id=0, node_id=1)
>>> target_multilayer_node = MultilayerNode(layer_id=1, node_id=2)
>>> im.add_multilayer_link(source_multilayer_node, target_multilayer_node)

Notes

This is the full multilayer format that supports both undirected and directed links. Infomap will not make any changes to the network.

Parameters:
  • source_multilayer_node (tuple of int, or MultilayerNode) – If passed a tuple, it should be of the format (layer_id, node_id).

  • target_multilayer_node (tuple of int, or MultilayerNode) – If passed a tuple, it should be of the format (layer_id, node_id).

  • weight (float, optional) –

Add several multilayer links.

Examples

>>> from infomap import Infomap
>>> im = Infomap()
>>> links = (
...     ((0, 1), (1, 2)),
...     ((0, 3), (1, 2))
... )
>>> im.add_multilayer_links(links)
Parameters:

links (iterable of tuples) – Iterable of tuples of the form (source_node, target_node, [weight])

add_networkx_graph(g, weight='weight')

Add NetworkX graph

Examples

>>> import networkx as nx
>>> from infomap import Infomap
>>> G = nx.Graph([("a", "b"), ("a", "c")])
>>> im = Infomap(silent=True)
>>> mapping = im.add_networkx_graph(G)
>>> mapping
{0: 'a', 1: 'b', 2: 'c'}
>>> im.run()
>>> for node in im.nodes:
...     print(node.node_id, node.module_id, node.flow, mapping[node.node_id])
0 1 0.5 a
1 1 0.25 b
2 1 0.25 c

Notes

Transforms non-int labels to unique int ids. Assumes that all nodes are of the same type. If node type is string, they are added as names to Infomap. If the NetworkX graph is directed (nx.DiGraph), and no flow model has been specified in the constructor, this method sets the directed flag to True.

Parameters:
  • g (nx.Graph) – A NetworkX graph

  • weight (str, optional) – Key to lookup link weight in edge data if present. Default "weight".

Returns:

Dict with the node ids as keys and labels as values.

Return type:

dict

add_node(node_id, name=None, teleportation_weight=None)

Add a node.

See also

set_name, add_nodes

Parameters:
  • node_id (int) –

  • name (str, optional) –

  • teleportation_weight (float, optional) – Used for teleporting between layers in multilayer networks.

add_nodes(nodes)

Add nodes.

See also

add_node

Examples

Add nodes

>>> from infomap import Infomap
>>> im = Infomap()
>>> im.add_nodes(range(4))

Add named nodes

>>> from infomap import Infomap
>>> im = Infomap()
>>> nodes = (
...     (1, "Node 1"),
...     (2, "Node 2"),
...     (3, "Node 3")
... )
>>> im.add_nodes(nodes)
>>> im.names
{1: 'Node 1', 2: 'Node 2', 3: 'Node 3'}

Add named nodes with teleportation weights

>>> from infomap import Infomap
>>> im = Infomap()
>>> nodes = (
...     (1, "Node 1", 0.5),
...     (2, "Node 2", 0.2),
...     (3, "Node 3", 0.8)
... )
>>> im.add_nodes(nodes)
>>> im.names
{1: 'Node 1', 2: 'Node 2', 3: 'Node 3'}

Add named nodes using dict

>>> from infomap import Infomap
>>> im = Infomap()
>>> nodes = {
...     1: "Node 1",
...     2: "Node 2",
...     3: "Node 3"
... }
>>> im.add_nodes(nodes)
>>> im.names
{1: 'Node 1', 2: 'Node 2', 3: 'Node 3'}

Add named nodes with teleporation weights using dict

>>> from infomap import Infomap
>>> im = Infomap()
>>> nodes = {
...     1: ("Node 1", 0.5),
...     2: ("Node 2", 0.2),
...     3: ("Node 3", 0.8)
... }
>>> im.add_nodes(nodes)
>>> im.names
{1: 'Node 1', 2: 'Node 2', 3: 'Node 3'}
Parameters:

nodes (iterable of tuples or iterable of int or dict of int: str or dict of int: tuple of (str, float)) – Iterable of tuples on the form (node_id, [name], [teleportation_weight])

add_state_node(state_id, node_id)

Add a state node.

Notes

If a physical node with id node_id does not exist, it will be created. If you want to name the physical node, use set_name.

Parameters:
  • state_id (int) –

  • node_id (int) – Id of the physical node the state node should be added to.

add_state_nodes(state_nodes)

Add state nodes.

See also

add_state_node

Examples

With tuples

>>> from infomap import Infomap
>>> im = Infomap()
>>> states = (
...     (1, 1),
...     (2, 1),
...     (3, 2)
... )
>>> im.add_state_nodes(states)

With dict

>>> from infomap import Infomap
>>> im = Infomap()
>>> states = {
...     1: 1,
...     2: 1,
...     3: 2
... }
>>> im.add_state_nodes(states)
Parameters:

state_nodes (iterable of tuples or dict of int: int) – Iterable of tuples of the form (state_id, node_id) or dict of the form {state_id: node_id}.

property bipartite_start_id

Get or set the bipartite start id.

Examples

>>> from infomap import Infomap
>>> im = Infomap(silent=True, num_trials=10)
>>> im.add_node(1, "Left 1")
>>> im.add_node(2, "Left 2")
>>> im.bipartite_start_id = 3
>>> im.add_node(3, "Right 3")
>>> im.add_node(4, "Right 4")
>>> im.add_link(1, 3)
>>> im.add_link(1, 4)
>>> im.add_link(2, 4)
>>> im.run()
>>> tol = 1e-4
>>> abs(im.codelength - 0.9182958340544896) < tol
True
Parameters:

start_id (int) – The node id where the second node type starts.

Returns:

The node id where the second node type starts.

Return type:

int

property codelength

Get the total (hierarchical) codelength.

Returns:

The codelength

Return type:

float

property codelengths

Get the total (hierarchical) codelength for each trial.

See also

codelength

Returns:

The codelengths for each trial

Return type:

tuple of float

property effective_num_leaf_modules

The flow weighted effective number of leaf modules.

Measured as the perplexity of the module flow distribution.

Returns:

The effective number of top modules

Return type:

float

property effective_num_top_modules

The flow weighted effective number of top modules.

Measured as the perplexity of the module flow distribution.

Returns:

The effective number of top modules

Return type:

float

property entropy_rate

Get the entropy rate of the network.

The entropy rate is an indication of the sparsity of a network. A higher entropy rate corresponds to a densely connected network.

Notes

This value is only accessable after running the optimizer (im.run()).

Examples

>>> from infomap import Infomap
>>> im = Infomap(silent=True, no_infomap=True)
>>> im.read_file("twotriangles.net")
>>> im.run()
>>> f"{im.entropy_rate:.5f}"
'1.25070'
Returns:

The entropy rate

Return type:

float

A view of the currently assigned links and their flow.

The sources and targets are state ids when we have a state or multilayer network.

Examples

>>> from infomap import Infomap
>>> im = Infomap(silent=True)
>>> im.read_file("twotriangles.net")
>>> im.run()
>>> for link in im.flow_links:
...     print(link)
(1, 2, 0.14285714285714285)
(1, 3, 0.14285714285714285)
(2, 3, 0.14285714285714285)
(3, 4, 0.14285714285714285)
(4, 5, 0.14285714285714285)
(4, 6, 0.14285714285714285)
(5, 6, 0.14285714285714285)

See also

links

Returns:

An iterator of source, target, flow tuples.

Return type:

tuple of int, int, float

get_dataframe(columns=['path', 'flow', 'name', 'node_id'])

Get a Pandas DataFrame with the selected columns.

Examples

>>> from infomap import Infomap
>>> im = Infomap(silent=True)
>>> im.read_file("twotriangles.net")
>>> im.run()
>>> im.get_dataframe()
     path      flow name  node_id
0  (1, 1)  0.214286    C        3
1  (1, 2)  0.142857    A        1
2  (1, 3)  0.142857    B        2
3  (2, 1)  0.214286    D        4
4  (2, 2)  0.142857    E        5
5  (2, 3)  0.142857    F        6
>>> im.get_dataframe(columns=["node_id", "module_id"])
   node_id  module_id
0        3          1
1        1          1
2        2          1
3        4          2
4        5          2
5        6          2
Parameters:

columns (list(str)) – A list of columns that should be extracted from each node. Must be available as an attribute of InfoNode, InfomapLeafIterator (for state nodes), or InfomapLeafIteratorPhysical. One exception to this is "name" which is looked up internally. Default ["path", "flow", "name", "node_id"].

Raises:
  • ImportError – If the pandas package is not available.

  • AttributeError – If a column name is not available as an InfoNode attribute.

Returns:

A DataFrame containing the selected columns.

Return type:

pandas.DataFrame

get_effective_num_modules(depth_level=1)

The flow weighted effective number of modules.

Measured as the perplexity of the module flow distribution.

Parameters:

depth_level (int, optional) – The module level returned by iterator.depth. Set to 1 (default) to return the top modules (coarsest level). Set to 2 for second coarsest level etc. Set to -1 to return the bottom level modules (finest level).

Returns:

The effective number of modules

Return type:

float

A view of the currently assigned links and their weights or flow.

The sources and targets are state ids when we have a state or multilayer network.

Examples

>>> from infomap import Infomap
>>> im = Infomap(silent=True)
>>> im.read_file("twotriangles.net")
>>> im.run()
>>> for link in im.get_links():
...     print(link)
(1, 2, 1.0)
(1, 3, 1.0)
(2, 3, 1.0)
(3, 4, 1.0)
(4, 5, 1.0)
(4, 6, 1.0)
(5, 6, 1.0)
>>> for link in im.get_links(data="flow"):
...     print(link)
(1, 2, 0.14285714285714285)
(1, 3, 0.14285714285714285)
(2, 3, 0.14285714285714285)
(3, 4, 0.14285714285714285)
(4, 5, 0.14285714285714285)
(4, 6, 0.14285714285714285)
(5, 6, 0.14285714285714285)

See also

links, flow_links

Parameters:

data (str) – The kind of data to return, one of "weight" or "flow". Default "weight".

Returns:

An iterator of source, target, weight/flow tuples.

Return type:

tuple of int, int, float

get_modules(depth_level=1, states=False)

Get a dict with node ids as keys and module ids as values for a given depth in the hierarchical tree.

Level                            Root

  0                               ┌─┐
                        ┌─────────┴─┴────────┐
                        │                    │
                        │                    │
                        │                    │
                  Path  │  Module      Path  │  Module
  1                  1 ┌┼┐ 1              2 ┌┼┐ 2
                   ┌───┴─┴───┐          ┌───┴─┴───┐
                   │         │          │         │
                   │         │          │         │
                   │         │          │         │
                   │         │          │         │
  2             1 ┌┼┐ 1   2 ┌┼┐ 2    1 ┌┼┐ 3   2 ┌┼┐ 3
              ┌───┴─┴───┐   └─┴────┐   └─┘       └─┘
              │         │          │
              │         │          │    ▲         ▲
              │         │          │    └────┬────┘
              │         │          │         │
  3        1 ┌┼┐     2 ┌┼┐      1 ┌┼┐
             └─┘       └─┘        └─┘  ◄───  Leaf-nodes

Path to the left of the nodes. Depth dependent module ids to the right. The five leaf-nodes are network-nodes. All other tree-nodes are modules.

For example:

The left-most node on level 3 has path 1:1:1 and belong to module 1 on level 1.

The right-most node on level 2 has path 2:2 and belong to module 2 on level 1 which is renamed to module 3 on level 2 as we have more modules in total on this level.

Assuming the nodes are labelled 1-5 from left to right, then the first three nodes are in module 1, and the last two nodes are in module 2:

> im.get_modules(depth_level=1)
{1: 1, 2: 1, 3: 1, 4: 2, 5: 2}

However, at level 2, the first two nodes are in module 1, the third node in module 2, and the last two nodes are in module 3:

> im.get_modules(depth_level=2)
{1: 1, 2: 1, 3: 2, 4: 3, 5: 3}

Examples

>>> from infomap import Infomap
>>> im = Infomap(silent=True)
>>> im.read_file("twotriangles.net")
>>> im.run()
>>> im.get_modules()
{1: 1, 2: 1, 3: 1, 4: 2, 5: 2, 6: 2}
>>> from infomap import Infomap
>>> im = Infomap(silent=True)
>>> im.read_file("states.net")
>>> im.run()
>>> im.get_modules(states=True)
{1: 1, 2: 1, 3: 1, 4: 2, 5: 2, 6: 2}

Notes

In a higher-order network, a physical node (defined by node_id) may partially exist in multiple modules. However, the node_id can not exist multiple times as a key in the node-to-module map, so only one occurrence of a physical node will be retrieved. To get all states, use get_modules(states=True).

Parameters:
  • depth_level (int, optional) – The level in the hierarchical tree. Set to 1 (default) to return the top modules (coarsest level). Set to 2 for second coarsest level etc. Set to -1 to return the bottom level modules (finest level). Default 1.

  • states (bool, optional) – For higher-order networks, if states is True, it will return state node ids. Otherwise it will return physical node ids, merging state nodes with same node_id if they are in the same module. Note that the same physical node may end up on different paths in the tree. Default false.

Returns:

Dict with node ids as keys and module ids as values.

Return type:

dict of int

get_multilevel_modules(states=False)

Get a dict with node ids as keys and a tuple of module ids as values. Each position in the tuple corresponds to a depth in the hierarchical tree, with the first level being the top level.

See also

get_modules

Examples

>>> from infomap import Infomap
>>> im = Infomap(silent=True, num_trials=10)
>>> im.read_file("ninetriangles.net")
>>> im.run()
>>> for modules in sorted(im.get_multilevel_modules().values()):
...     print(modules)
(1, 1)
(1, 1)
(1, 1)
(1, 2)
(1, 2)
(1, 2)
(1, 3)
(1, 3)
(1, 3)
(2, 4)
(2, 4)
(2, 4)
(2, 5)
(2, 5)
(2, 5)
(2, 6)
(2, 6)
(2, 6)
(3, 7)
(3, 7)
(3, 7)
(4, 8)
(4, 8)
(4, 8)
(5, 9)
(5, 9)
(5, 9)
>>> from infomap import Infomap
>>> im = Infomap(silent=True)
>>> im.read_file("states.net")
>>> im.run()
>>> for node, modules in im.get_multilevel_modules(states=True).items():
...     print(node, modules)
1 (1,)
2 (1,)
3 (1,)
4 (2,)
5 (2,)
6 (2,)

Notes

In a higher-order network, a physical node (defined by node_id) may partially exist in multiple modules. However, the node_id can not exist multiple times as a key in the node-to-module map, so only one occurrence of a physical node will be retrieved. To get all states, use get_multilevel_modules(states=True).

Parameters:

states (bool, optional) – For higher-order networks, if states is True, it will return state node ids. Otherwise it will return physical node ids, merging state nodes with same node_id if they are in the same module. Note that the same physical node may end up on different paths in the tree. Default false.

Returns:

Dict with node ids as keys and tuple of module ids as values.

Return type:

dict of list of int

get_name(node_id, default=None)

Get the name of a node.

Notes

If the node name is an empty string, the default will be returned.

See also

set_name, names

Parameters:
  • node_id (int) –

  • default (str, optional) – The return value if the node name is missing, default None

Returns:

The node name if it exists, else the default.

Return type:

str

get_names()

Get all node names.

See also

names, get_name

Returns:

A dict with node ids as keys and node names as values.

Return type:

dict of string

get_nodes(depth_level=1, states=False)

A view of the nodes in the hierarchical tree, iterating depth first from the root.

Parameters:
  • depth_level (int, optional) – The module level returned by iterator.module_id. Set to 1 (default) to return the top modules (coarsest level). Set to 2 for second coarsest level etc. Set to -1 to return the bottom level modules (finest level). Default 1.

  • states (bool, optional) – For higher-order networks, if states is True, it will iterate over state nodes. Otherwise it will iterate over physical nodes, merging state nodes with same node_id if they are in the same module. Note that the same physical node may end up on different paths in the tree. See notes on physical_tree. Default false.

Notes

For higher-order networks, each node is represented by a set of state nodes with the same node_id, where each state node represents a different constraint on the random walker. This enables overlapping modules, where state nodes with the same node_id end up in different modules. However, the state nodes with the same node_id within each module are only visible as one (partial) physical node (if states = False).

Returns:

An iterator over each node in the tree, depth first from the root

Return type:

InfomapIterator or InfomapIteratorPhysical

get_tree(depth_level=1, states=False)

A view of the hierarchical tree, iterating over the modules as well as the leaf-nodes.

Parameters:
  • depth_level (int, optional) – The module level returned by iterator.module_id. Set to 1 (default) to return the top modules (coarsest level). Set to 2 for second coarsest level etc. Set to -1 to return the bottom level modules (finest level).

  • states (bool, optional) – For higher-order networks, if states is True, it will iterate over state nodes. Otherwise it will iterate over physical nodes, merging state nodes with same node_id if they are in the same module. Note that the same physical node may end up on different paths in the tree. Default false.

Notes

For higher-order networks, each node is represented by a set of state nodes with the same node_id, where each state node represents a different constraint on the random walker. This enables overlapping modules, where state nodes with the same node_id end up in different modules. However, the state nodes with the same node_id within each module are only visible as one (partial) physical node (if states = False).

Returns:

An iterator over each node in the tree, depth first from the root

Return type:

InfomapIterator or InfomapIteratorPhysical

property have_memory

Returns true for multilayer and memory networks.

Returns:

True if the network is a multilayer or memory network.

Return type:

bool

property index_codelength

Get the two-level index codelength.

Returns:

The two-level index codelength

Return type:

float

property initial_partition

Get or set the initial partition.

This is a initial configuration of nodes into modules where Infomap will start the optimizer.

Examples

>>> from infomap import Infomap
>>> im = Infomap(silent=True)
>>> im.add_node(1)
>>> im.add_node(2)
>>> im.add_node(3)
>>> im.add_node(4)
>>> im.add_link(1, 2)
>>> im.add_link(1, 3)
>>> im.add_link(2, 3)
>>> im.add_link(2, 4)
>>> im.initial_partition = {
...     1: 0,
...     2: 0,
...     3: 1,
...     4: 1
... }
>>> im.run(no_infomap=True)
>>> tol = 1e-4
>>> abs(im.codelength - 3.4056390622295662) < tol
True

Notes

The initial partition is saved between runs. If you want to use an initial partition for one run only, use run(initial_partition=partition).

Parameters:

module_ids (dict of int, or None) – Dict with node ids as keys and module ids as values.

Returns:

Dict with node ids as keys and module ids as values.

Return type:

dict of int

property leaf_modules

A view of the leaf modules, i.e. the bottom modules containing leaf nodes.

Returns:

An iterator over each leaf module in the tree, depth first from the root

Return type:

InfomapLeafModuleIterator

A view of the currently assigned links and their weights.

The sources and targets are state ids when we have a state or multilayer network.

Examples

>>> from infomap import Infomap
>>> im = Infomap(silent=True)
>>> im.read_file("twotriangles.net")
>>> im.run()
>>> for link in im.links:
...     print(link)
(1, 2, 1.0)
(1, 3, 1.0)
(2, 3, 1.0)
(3, 4, 1.0)
(4, 5, 1.0)
(4, 6, 1.0)
(5, 6, 1.0)

See also

flow_links

Returns:

An iterator of source, target, weight tuples.

Return type:

tuple of int, int, float

property max_depth

Get the max depth of the hierarchical tree.

Returns:

The max depth

Return type:

int

property meta_codelength

Get the meta codelength.

This is the meta entropy times the meta data rate.

See also

meta_entropy

Returns:

The meta codelength

Return type:

float

property meta_entropy

Get the meta entropy (unweighted by meta data rate).

See also

meta_codelength

Returns:

The meta entropy

Return type:

float

property module_codelength

Get the total codelength of the modules.

The module codelength is defined such that codelength = index_codelength + module_codelength

For a hierarchical solution, the module codelength is the sum of codelengths for each top module.

Returns:

The module codelength

Return type:

float

property modules

A view of the top-level modules, mapping node_id to module_id.

Notes

In a higher-order network, a physical node (defined by node_id) may partially exist in multiple modules. However, the node_id can not exist multiple times as a key in the node-to-module map, so only one occurrence of a physical node will be retrieved. To get all states, use get_modules(states=True).

Examples

>>> from infomap import Infomap
>>> im = Infomap(silent=True, num_trials=5)
>>> im.read_file("twotriangles.net")
>>> im.run()
>>> for node_id, module_id in im.modules:
...     print(node_id, module_id)
...
1 1
2 1
3 1
4 2
5 2
6 2

See also

get_modules

Yields:

tuple of int, int – An iterator of (node_id, module_id) pairs.

property multilevel_modules

A view of the multilevel modules, mapping node_id to a tuple of module_id.

Notes

In a higher-order network, a physical node (defined by node_id) may partially exist in multiple modules. However, the node_id can not exist multiple times as a key in the node-to-module map, so only one occurrence of a physical node will be retrieved. To get all states, use get_multilevel_modules(states=True).

Yields:

tuple of (int, tuple of int) – An iterator of (node_id, (module_ids...) pairs.

property names

Get all node names.

Short-hand for get_names.

See also

get_names, get_name

Returns:

A dict with node ids as keys and node names as values.

Return type:

dict of string

property network

Get the internal network.

property nodes

A view of the nodes in the hierarchical tree, iterating depth first from the root.

Convinience method for get_nodes(depth_level=1, states=True).

Returns:

An iterator over each leaf node in the tree, depth first from the root

Return type:

InfomapLeafIterator

property num_leaf_modules

Get the number of leaf modules in the tree

Returns:

The number of leaf modules

Return type:

int

property num_levels

Get the max depth of the hierarchical tree. Alias of max_depth.

See also

max_depth

Returns:

The max depth

Return type:

int

The number of links.

Returns:

The number of links

Return type:

int

property num_nodes

The number of state nodes if we have a higher order network, or the number of physical nodes.

Returns:

The number of nodes

Return type:

int

property num_non_trivial_top_modules

Get the number of non-trivial top modules in the tree

A trivial module is a module with either one or all nodes within.

Returns:

The number of non-trivial top modules

Return type:

int

property num_physical_nodes

The number of physical nodes.

See also

num_nodes

Returns:

The number of nodes

Return type:

int

property num_top_modules

Get the number of top modules in the tree

Returns:

The number of top modules

Return type:

int

property one_level_codelength

Get the one-level codelength.

See also

codelength

Returns:

The one-level codelength

Return type:

float

property physical_nodes

A view of the nodes in the hierarchical tree, iterating depth first from the root. All state nodes with the same node_id are merged to one physical node.

Convinience method for get_nodes(depth_level=1, states=False).

Returns:

An iterator over each physical leaf node in the tree, depth first from the root

Return type:

InfomapLeafIteratorPhysical

property physical_tree

A view of the hierarchical tree, iterating over the modules as well as the leaf-nodes. All state nodes with the same node_id are merged to one physical node.

Convinience method for get_tree(depth_level=1, states=False).

Returns:

An iterator over each physical node in the tree, depth first from the root

Return type:

InfomapIteratorPhysical

read_file(filename, accumulate=True)

Read network data from file.

Parameters:
  • filename (str) –

  • accumulate (bool, optional) – If the network data should be accumulated to already added nodes and links. Default True.

property relative_codelength_savings

Get the relative codelength savings.

This is defined as the reduction in codelength relative to the non-modular one-level solution:

S_L = 1 - L / L_1

where L is the codelength and L_1 the one_level_codelength.

Returns:

The relative codelength savings

Return type:

float

Remove a link.

Notes

Removing links will not remove nodes if they become disconnected.

See also

add_link

Parameters:
  • source_id (int) –

  • target_id (int) –

Remove several links.

Examples

>>> from infomap import Infomap
>>> im = Infomap()
>>> links = (
...     (1, 2),
...     (1, 3)
... )
>>> im.add_links(links)
>>> im.remove_links(links)
>>> im.num_links
0

See also

remove_link

Parameters:

links (iterable of tuples) – Iterable of tuples of the form (source_id, target_id)

run(args=None, initial_partition=None, cluster_data=None, no_infomap=False, skip_adjust_bipartite_flow=False, bipartite_teleportation=False, weight_threshold=None, include_self_links=None, no_self_links=False, node_limit=None, matchable_multilayer_ids=None, assign_to_neighbouring_module=False, meta_data=None, meta_data_rate=1.0, meta_data_unweighted=False, tree=False, ftree=False, clu=False, verbosity_level=1, silent=False, out_name=None, no_file_output=False, clu_level=None, output=None, hide_bipartite_nodes=False, print_all_trials=False, two_level=False, flow_model=None, directed=None, recorded_teleportation=False, use_node_weights_as_flow=False, to_nodes=False, teleportation_probability=0.15, regularized=False, regularization_strength=1.0, entropy_corrected=False, entropy_correction_strength=1.0, markov_time=1.0, variable_markov_time=False, variable_markov_damping=1.0, preferred_number_of_modules=None, multilayer_relax_rate=0.15, multilayer_relax_limit=-1, multilayer_relax_limit_up=-1, multilayer_relax_limit_down=-1, multilayer_relax_by_jsd=False, seed=123, num_trials=1, core_loop_limit=10, core_level_limit=None, tune_iteration_limit=None, core_loop_codelength_threshold=1e-10, tune_iteration_relative_threshold=1e-05, fast_hierarchical_solution=None, prefer_modular_solution=False, inner_parallelization=False)

Run Infomap.

Parameters:
  • args (str, optional) – String of Infomap arguments.

  • initial_partition (dict, optional) – Initial partition to start optimizer from. (See initial_partition).

  • cluster_data (str, optional) – Provide an initial two-level (clu format) or multi-layer (tree format) solution.

  • no_infomap (bool, optional) – Don’t run the optimizer. Useful to calculate codelength of provided cluster data or to print non-modular statistics.

  • skip_adjust_bipartite_flow (bool, optional) – Skip distributing all flow from the bipartite nodes to the primary nodes.

  • bipartite_teleportation (bool, optional) – Teleport like the bipartite flow instead of two-step (unipartite) teleportation.

  • weight_threshold (float, optional) – Limit the number of links to read from the network. Ignore links with less weight than the threshold.

  • include_self_links (bool, optional) – Include links with the same source and target node. DEPRECATED. Include self links by default now, exclude with no_self_links.

  • no_self_links (bool, optional) – Exclude self links in the input network.

  • node_limit (int, optional) – Limit the number of nodes to read from the network. Ignore links connected to ignored nodes.

  • matchable_multilayer_ids (int, optional) – Construct state ids from node and layer ids that are consistent across networks for the same max number of layers. Set to at least the largest layer id among networks to match.

  • assign_to_neighbouring_module (bool, optional) – Assign nodes without module assignments (from cluster_data) to the module assignment of a neighbouring node if possible.

  • meta_data (str, optional) – Provide meta data (clu format) that should be encoded.

  • meta_data_rate (float, optional) – Metadata encoding rate. Default is to encode each step.

  • meta_data_unweighted (bool, optional) – Don’t weight meta data by node flow.

  • tree (bool, optional) – Write a tree file with the modular hierarchy. Automatically enabled if no other output is specified.

  • ftree (bool, optional) – Write a ftree file with the modular hierarchy including aggregated links between (nested) modules.

  • clu (bool, optional) – Write a clu file with the top cluster ids for each node.

  • verbosity_level (int, optional) – Verbose output on the console.

  • silent (bool, optional) – No output on the console.

  • out_name (str, optional) – Name for the output files, e.g. "[output_directory]/[out-name].tree"

  • no_file_output (bool, optional) – Don’t write output to file.

  • clu_level (int, optional) – For clu output, print modules at specified depth from root. Use -1 for bottom level modules.

  • output (list(str), optional) – List of output formats. Options: clu, tree, ftree, newick, json, csv, network, states.

  • hide_bipartite_nodes (bool, optional) – Project bipartite solution to unipartite.

  • print_all_trials (bool, optional) – Print all trials to separate files.

  • two_level (bool, optional) – Optimize a two-level partition of the network. Default (false) is multi-level.

  • flow_model (str, optional) – Specify flow model. Options: undirected, directed, undirdir, outdirdir, rawdir.

  • directed (bool, optional) – Assume directed links. Shorthand for flow_model="directed".

  • recorded_teleportation (bool, optional) – If teleportation is used to calculate the flow, also record it when minimizing codelength. Default False.

  • use_node_weights_as_flow (bool, optional) – Use node weights (from api or after names in Pajek format) as flow, normalized to sum to 1.

  • to_nodes (bool, optional) – Teleport to nodes instead of to links, assuming uniform node weights if no such input data.

  • teleportation_probability (float, optional) – Probability of teleporting to a random node or link.

  • regularized (bool, optional) – Effectively add a fully connected Bayesian prior network to not overfit due to missing links. Implies recorded teleportation.

  • regularization_strength (float, optional) – Adjust relative strength of Bayesian prior network with this multiplier.

  • entropy_corrected (bool, optional) – Correct for negative entropy bias in small samples (many modules).

  • entropy_correction_strength (float, optional) – Increase or decrease the default entropy correction with this multiplier.

  • markov_time (float, optional) – Scales link flow to change the cost of moving between modules. Higher values results in fewer modules.

  • variable_markov_time (bool, optional) – Increase Markov time locally to level out link flow. Reduces risk of overpartitioning sparse areas while keeping high resolution in dense areas.

  • variable_markov_damping (float, optional) – Exponent for variable Markov time scale. 0 means no rescaling and 1 means full rescaling to constant transition flow rate.

  • preferred_number_of_modules (int, optional) – Penalize solutions the more they differ from this number.

  • multilayer_relax_rate (float, optional) – Probability to relax the constraint to move only in the current layer.

  • multilayer_relax_limit (int, optional) – Number of neighboring layers in each direction to relax to. If negative, relax to any layer.

  • multilayer_relax_limit_up (int, optional) – Number of neighboring layers with higher id to relax to. If negative, relax to any layer.

  • multilayer_relax_limit_down (int, optional) – Number of neighboring layers with lower id to relax to. If negative, relax to any layer.

  • multilayer_relax_by_jsd (bool, optional) – Relax proportional to the out-link similarity measured by the Jensen-Shannon divergence.

  • seed (int, optional) – A seed (integer) to the random number generator for reproducible results.

  • num_trials (int, optional) – Number of outer-most loops to run before picking the best solution.

  • core_loop_limit (int, optional) – Limit the number of loops that tries to move each node into the best possible module.

  • core_level_limit (int, optional) – Limit the number of times the core loops are reapplied on existing modular network to search bigger structures.

  • tune_iteration_limit (int, optional) – Limit the number of main iterations in the two-level partition algorithm. 0 means no limit.

  • core_loop_codelength_threshold (float, optional) – Minimum codelength threshold for accepting a new solution in core loop.

  • tune_iteration_relative_threshold (float, optional) – Set codelength improvement threshold of each new tune iteration to f times the initial two-level codelength.

  • fast_hierarchical_solution (int, optional) – Find top modules fast. Use 2 to keep all fast levels. Use 3 to skip recursive part.

  • prefer_modular_solution (bool, optional) – Prefer modular solutions even if they are worse than putting all nodes in one module.

  • inner_parallelization (bool, optional) – Parallelize the inner-most loop for greater speed. This may give some accuracy tradeoff.

set_meta_data(node_id, meta_category)

Set meta data to a node.

Examples

>>> from infomap import Infomap
>>> im = Infomap(silent=True, num_trials=10)
>>> im.add_links((
...     (1, 2), (1, 3), (2, 3),
...     (3, 4),
...     (4, 5), (4, 6), (5, 6)
... ))
>>> im.set_meta_data(1, 0)
>>> im.set_meta_data(2, 0)
>>> im.set_meta_data(3, 1)
>>> im.set_meta_data(4, 1)
>>> im.set_meta_data(5, 0)
>>> im.set_meta_data(6, 0)
>>> im.run(meta_data_rate=0)
>>> im.num_top_modules
2
>>> im.run(meta_data_rate=2)
>>> im.num_top_modules
3
Parameters:
  • node_id (int) –

  • meta_category (int) –

set_name(node_id, name)

Set the name of a node.

Parameters:
  • node_id (int) –

  • name (str) –

set_names(names)

Set names to several nodes at once.

Examples

With tuples

>>> from infomap import Infomap
>>> im = Infomap()
>>> names = (
...     (1, "Node 1"),
...     (2, "Node 2")
... )
>>> im.set_names(names)
>>> im.names
{1: 'Node 1', 2: 'Node 2'}

With dict

>>> from infomap import Infomap
>>> im = Infomap()
>>> names = {
...     1: "Node 1",
...     2: "Node 2"
... }
>>> im.set_names(names)
>>> im.names
{1: 'Node 1', 2: 'Node 2'}

See also

set_name, names

Parameters:

names (iterable of tuples or dict of int: str) – Iterable of tuples on the form (node_id, name) or dict of the form {node_id: name}.

property tree

A view of the hierarchical tree, iterating over the modules as well as the leaf-nodes.

Convinience method for get_tree(depth_level=1, states=True).

Returns:

An iterator over each node in the tree, depth first from the root

Return type:

InfomapIterator

write(filename, *args, **kwargs)

Write results to file.

Raises:

NotImplementedError – If the file format is not supported.

Parameters:

filename (str) – The filename.

write_clu(filename, states=False, depth_level=1)

Write result to a clu file.

Parameters:
  • filename (str) –

  • states (bool, optional) – If the state nodes should be included. Default False.

  • depth_level (int, optional) – The depth in the hierarchical tree to write.

write_csv(filename, states=False)

Write result to a CSV file.

See also

write_clu, write_tree

Parameters:
  • filename (str) –

  • states (bool, optional) – If the state nodes should be included. Default False.

write_flow_tree(filename, states=False)

Write result to a ftree file.

See also

write_clu, write_tree

Parameters:
  • filename (str) –

  • states (bool, optional) – If the state nodes should be included. Default False.

write_json(filename, states=False)

Write result to a JSON file.

See also

write_clu, write_tree

Parameters:
  • filename (str) –

  • states (bool, optional) – If the state nodes should be included. Default False.

write_newick(filename, states=False)

Write result to a Newick file.

See also

write_clu, write_tree

Parameters:
  • filename (str) –

  • states (bool, optional) – If the state nodes should be included. Default False.

write_pajek(filename, flow=False)

Write network to a Pajek file.

Parameters:
  • filename (str) –

  • flow (bool, optional) – If the flow should be included. Default False.

write_state_network(filename)

Write internal state network to file.

See also

write_pajek

Parameters:

filename (str) –

write_tree(filename, states=False)

Write result to a tree file.

Parameters:
  • filename (str) –

  • states (bool, optional) – If the state nodes should be included. Default False.

class infomap.MultilayerNode(layer_id, node_id)

Bases: tuple

layer_id

Alias for field number 0

node_id

Alias for field number 1

class infomap.InfoNode(*args)
property child_degree

The number of children.

Returns:

Number of children

Return type:

int

property flow

Get the flow of the node.

Returns:

The flow

Return type:

float

get_meta_data(dimension=0)

Get meta data on a specific dimension.

Parameters:

dimension (int) – The dimension (default 0)

Returns:

The meta data

Return type:

int

property is_leaf

True if the node has no children.

Returns:

Is leaf node

Return type:

bool

property is_leaf_module

True if the node has children but no grandchildren.

Returns:

Is leaf module

Return type:

bool

property is_root

True if the node has no parent.

Returns:

Is root

Return type:

bool

property layer_id

Get the layer id of a multilayer node.

Returns:

The layer id

Return type:

int

property meta_data

Meta data (on first dimension if more).

Returns:

The meta data

Return type:

int

property node_id

Get the physical node id.

Returns:

The node id

Return type:

int

property state_id

Get the state id of the node.

Returns:

The state id

Return type:

int

class infomap.InfomapIterator(*args)
property child_index

Get the child index.

Returns:

The child index

Return type:

int

property depth

Get the depth.

Returns:

The depth

Return type:

int

property modular_centrality

Get the modular centrality of the node.

Returns:

The modular centrality

Return type:

float

property module_id

Get the module id of the node.

Returns:

The module id

Return type:

int

property path

Get the path to the node in the tree.

Returns:

The path

Return type:

tuple of ints

class infomap.InfomapLeafModuleIterator(*args)
property child_index

Get the child index.

Returns:

The child index

Return type:

int

property depth

Get the depth.

Returns:

The depth

Return type:

int

property modular_centrality

Get the modular centrality of the node.

Returns:

The modular centrality

Return type:

float

property module_id

Get the module id of the node.

Returns:

The module id

Return type:

int

property path

Get the path to the node in the tree.

Returns:

The path

Return type:

tuple of ints

class infomap.InfomapLeafIterator(*args)
property child_index

Get the child index.

Returns:

The child index

Return type:

int

property depth

Get the depth.

Returns:

The depth

Return type:

int

property modular_centrality

Get the modular centrality of the node.

Returns:

The modular centrality

Return type:

float

property module_id

Get the module id of the node.

Returns:

The module id

Return type:

int

property path

Get the path to the node in the tree.

Returns:

The path

Return type:

tuple of ints

class infomap.InfomapIteratorPhysical(*args)
property child_index

Get the child index.

Returns:

The child index

Return type:

int

property depth

Get the depth.

Returns:

The depth

Return type:

int

property modular_centrality

Get the modular centrality of the node.

Returns:

The modular centrality

Return type:

float

property module_id

Get the module id of the node.

Returns:

The module id

Return type:

int

property path

Get the path to the node in the tree.

Returns:

The path

Return type:

tuple of ints

class infomap.InfomapLeafIteratorPhysical(*args)
property child_index

Get the child index.

Returns:

The child index

Return type:

int

property depth

Get the depth.

Returns:

The depth

Return type:

int

property modular_centrality

Get the modular centrality of the node.

Returns:

The modular centrality

Return type:

float

property module_id

Get the module id of the node.

Returns:

The module id

Return type:

int

property path

Get the path to the node in the tree.

Returns:

The path

Return type:

tuple of ints