Pelote

Pelote is a python library full of graph-related functions that can be used to complement networkx for higher-level tasks.

It mainly helps with the following things:

• Conversion of tabular data to graphs (bipartites, citation etc. in the spirit of Table2Net)
• Conversion of graphs to tabular data
• Monopartite projections of bipartite graphs
• Miscellaneous graph helper functions (filtering out nodes, edges etc.)
• Sparsification of graphs
• Reading & writing of graph formats not found in networkx (such as graphology JSON)

As such it is the perfect companion to ipysigma, our Jupyter widget that can render interactive graphs directly within your notebooks.

Installation

You can install pelote with pip with the following command:

pip install pelote

If you want to be able to use the library with pandas, you will need to install it also:

pip install pandas

Usage

• Tabular data to graphs
  • table_to_bipartite_graph
• Graphs to tabular data
  • graph_to_nodes_dataframe
  • graph_to_edges_dataframe
  • graph_to_dataframes
• Graph projection
  • monopartite_projection
• Graph sparsification
  • global_threshold_sparsification
  • multiscale_backbone
• Miscellaneous graph-related metrics
  • edge_disparity
• Graph utilities
  • largest_connected_component
  • crop_to_largest_connected_component
  • remove_edges
  • filter_edges
• Learning
  • floatsam_threshold_learner
• Reading & Writing
  • read_graphology_json

Tabular data to graphs

table_to_bipartite_graph

Function creating a bipartite graph from the given tabular data.

Arguments

• table Iterable[Indexable] or pd.DataFrame - input tabular data. It can be a large variety of things as long as it is 1. iterable and 2. yields indexable values such as dicts or lists. This can for instance be a list of dicts, a csv.DictReader stream etc. It also supports pandas DataFrame if the library is installed.
• first_part_col str or int - the name of the column containing the value representing a node in the resulting graph's first part. It could be the index if your rows are lists or a key if your rows are dicts instead.
• second_par_col str or int - the name of the column containing the value representing a node in the resulting graph's second part. It could be the index if your rows are lists or a key if your rows are dicts instead.
• node_part_attr str, optional "part" - name of the node attribute containing the part it belongs to.
• edge_weight_attr str, optional "weight" - name of the edge attribute containing its weight, i.e. the number of times it was found in the table.
• first_part_data Sequence or Callable, optional None - sequence (i.e. list, tuple etc.) of column from rows to keep as node attributes for the graph's first part. Can also be a function returning a dict of those attributes. Note that the first row containing a given node will take precedence over subsequent ones regarding data to include.
• second_part_data Sequence or Callable, optional None - sequence (i.e. list, tuple etc.) of column from rows to keep as node attributes for the graph's second part. Can also be a function returning a dict of those attributes. Note that the first row containing a given node will take precedence over subsequent ones regarding data to include.
• disjoint_keys bool, optional False - set this to True as an optimization mechanism if you know your part keys are disjoint, i.e. if no value for first_part_col can also be found in second_part_col. If you enable this option wrongly, the result can be incorrect.

Graphs to tabular data

graph_to_nodes_dataframe

Function converting the given networkx graph into a pandas DataFrame of its nodes.

from pelote import to_nodes_dataframe

df = to_nodes_dataframe(graph)

Arguments

• nx.AnyGraph - a networkx graph instance
• node_key_col str, optional "key" - name of the DataFrame column containing the node keys. If None, the node keys will be used as the DataFrame index.

Returns

pd.DataFrame - A pandas DataFrame

graph_to_edges_dataframe

Function converting the given networkx graph into a pandas DataFrame of its edges.

Arguments

• nx.AnyGraph - a networkx graph instance
• edge_source_col str, optional "source" - name of the DataFrame column containing the edge source.
• edge_target_col str, optional "target" - name of the DataFrame column containing the edge target.
• source_node_data Iterable or Mapping, optional None - iterable of attribute names or mapping from attribute names to column name to be used to add columns to the resulting dataframe based on source node data.
• target_node_data Iterable or Mapping, optional None - iterable of attribute names or mapping from attribute names to column name to be used to add columns to the resulting dataframe based on target node data.

Returns

pd.DataFrame - A pandas DataFrame

graph_to_dataframes

Function converting the given networkx graph into two pandas DataFrames: one for its nodes, one for its edges.

Arguments

• nx.AnyGraph - a networkx graph instance
• node_key_col str, optional "key" - name of the node DataFrame column containing the node keys. If None, the node keys will be used as the DataFrame index.
• edge_source_col str, optional "source" - name of the edge DataFrame column containing the edge source.
• edge_target_col str, optional "target" - name of the edge DataFrame column containing the edge target.
• source_node_data Iterable or Mapping, optional None - iterable of attribute names or mapping from attribute names to column name to be used to add columns to the edge dataframe based on source node data.
• target_node_data Iterable or Mapping, optional None - iterable of attribute names or mapping from attribute names to column name to be used to add columns to the edge dataframe based on target node data.

Returns

None - (pd.DataFrame, pd.DataFrame)

Graph projection

monopartite_projection

Function returning the monopartite projection of a given bipartite graph wrt one of both partitions of the graph.

That is to say the resulting graph will keep a single type of nodes sharing weighted edges based on the neighbors they shared in the bipartite graph.

import networkx as nx
from pelote import monopartite_projection

bipartite = nx.Graph()
bipartite.add_nodes_from([1, 2, 3], part='account')
bipartite.add_nodes_from([4, 5, 6], part='color')
bipartite.add_edges_from([
    (1, 4),
    (1, 5),
    (2, 6),
    (3, 4),
    (3, 6)
])

# Resulting graph will only contain nodes [1, 2, 3]
# with edges: (1, 3) and (2, 3)
monopartite = monopartite_projection(bipartite, 'account')

Arguments

• bipartite_graph nx.AnyGraph - target graph. The function will raise if given graph is not truly bipartite.
• part_to_keep Hashable or Collection - partition to keep in the projected graph. It can either be the value of the part node attribute in the given graph (a string, most commonly), or a collection (a set, list etc.) holding the nodes composing the part to keep.
• node_part_attr str, optional "part" - name of the node attribute containing the part the node belongs to.
• edge_weight_attr str, optional "weight" - name of the edge attribute containing the edge's weight.
• metric str, optional None - one of "jaccard", "overlap", "cosine", "dice" or "binary_cosine". If not given, resulting weight will be seyto the size of neighbor intersection.
• bipartition_check bool, optional True - whether to check if given graph is truly bipartite. You can disable this as an optimization strategy if you know what you are doing.
• weight_threshold float, optional None - if an edge weight should be less than this threshold we would not add it to the projected monopartite graph.

Returns

nx.Graph - the projected monopartite graph.

Graph sparsification

global_threshold_sparsification

Function returning a copy of the given graph without edges whose weight is less than a given threshold.

Arguments

• graph nx.AnyGraph - target graph.
• weight_threshold float - weight threshold.
• reverse bool, optional - whether to reverse the threshold condition. That is to say an edge would be removed if its weight is greater than the threshold.

Returns

nx.AnyGraph - the sparse graph.

multiscale_backbone

Function returning the multiscale backbone of the given graph, i.e. a copy of the graph were we only kept "relevant" edges, as defined by a statistical test where we compare the likelihood of a weighted edge existing vs. the null model.

Article: Serrano, M. Ángeles, Marián Boguná, and Alessandro Vespignani. "Extracting the multiscale backbone of complex weighted networks." Proceedings of the national academy of sciences 106.16 (2009): 6483-6488.

References: - https://www.pnas.org/content/pnas/106/16/6483.full.pdf - https://en.wikipedia.org/wiki/Disparity_filter_algorithm_of_weighted_network

Arguments

• graph nx.AnyGraph - target graph.
• alpha float, optional 0.05 - alpha value for the statistical test. It can be intuitively thought of as a p-value score for an edge to be kept in the resulting graph.
• edge_weight_attr str, optional "weight" - name of the edge attribute holding the edge's weight.

Returns

nx.AnyGraph - the sparse graph.

Miscellaneous graph-related metrics

edge_disparity

Function computing the disparity score of each edge in the given graph. This score is typically used to extract the multiscale backbone of a weighted graph.

Arguments

• graph nx.AnyGraph - target graph.
• edge_weight_attr str, optional "weight" - name of the edge attribute containing its weight.
• reverse bool, optional False - whether to reverse the metric, i.e. return 1 - score.

Returns

dict - Dictionnary with edges - (source, target) tuples - as keys and the disparity scores as values

Graph utilities

largest_connected_component

Function returning the largest connected component of given networkx graph as a set of nodes.

Note that this function will consider any given graph as undirected and will therefore work with weakly connected components in the directed case.

Arguments

• graph nx.AnyGraph - target graph.

Returns

set - set of nodes representing the largest connected component.

crop_to_largest_connected_component

Function mutating the given networkx graph in order to keep only the largest connected component.

Note that this function will consider any given graph as undirected and will therefore work with weakly connected components in the directed case.

Arguments

• graph nx.AnyGraph - target graph.

remove_edges

Function removing all edges that do not pass a predicate function from a given networkx graph.

Note that this function mutates the given graph.

Arguments

• graph nx.AnyGraph - a networkx graph.
• predicate callable - a function taking each edge source, target and attributes and returning True if you want to keep the edge or False if you want to remove it.

filter_edges

Function returning a copy of the given networkx graph but without the edges filtered out by the given predicate function

Arguments

• graph nx.AnyGraph - a networkx graph.
• predicate callable - a function taking each edge source, target and attributes and returning True if you want to keep the edge or False if you want to remove it.

Returns

nx.AnyGraph - the filtered graph.

Learning

floatsam_threshold_learner

Function using an iterative algorithm to try and find the best weight threshold to apply to trim the given graph's edges while keeping the underlying community structure.

It works by iteratively increasing the threshold and stopping as soon as a significant connected component starts to drift away from the principal one.

This is basically an optimization algorithm applied to a complex nonlinear function using a very naive cost heuristic, but it works decently for typical cases as it emulates the method used by hand by some researchers when they perform this kind of task on Gephi, for instance.

Arguments

• graph nx.Graph - Graph to sparsify.
• starting_treshold float, optional 0.0 - Starting similarity threshold.
• learning_rate float, optional 0.05 - How much to increase the threshold at each step of the algorithm.
• max_drifter_order int, optional - Max order of component to detach itself from the principal one before stopping the algorithm. If not provided it will default to the logarithm of the graph's largest connected component's order.
• edge_weight_attr str, optional "weight" - Name of the weight attribute.

Returns

float - The found threshold

Reading & Writing

read_graphology_json

Function reading and parsing the given json file as a networkx graph.

Arguments

• target str or Path or file or dict - target to read and parse. Can be a string path, a Path instance, a file buffer or already parsed JSON data as a dict.

Returns

nx.AnyGraph - a networkx graph instance.