Graphs

Generators

A collection of graph generators.

All the graph generators here create a networkx.Graph instance with integer node labels increasing from the center (the central node will have index equal to 0).

er.graph.generator.from_matfile(filename, adj_key='C', nodes_key='nodes')

Generates a graph based on a Matlab file (.mat).

The Matlab file must contain the adjacency matrix (C) and a list of node coordinates (nodes).

Args:

filename: The path to the .mat file. adj_key: The name of the cell containing the adjacency matrix. nodes_key: The name of the cell containing the nodes.

Returns:

A networkx.Graph instance.

er.graph.generator.hexagonal_lattice(num_nodes, periodic=False)

Generates an hexagonal lattice graph with about num_nodes nodes.

Args:

num_nodes: The desired number of nodes. Note that the produced lattice

may not have the exact number of nodes specified.

periodic: Whether the generated lattice should be periodic (the nodes on

the contour will be connected each other). False by default.

Returns:

A networkx.Graph instance.

er.graph.generator.random_regular(num_nodes)

Generates a random 3-regular graph with num_nodes nodes.

Args:

num_nodes: The desired number of nodes in the graph.

Returns:

A networkx.Graph instance.

Trajectory

class er.graph.Trajectory(nodes, times=None, id=None)

Trajectory represents a path on a graph.

append(node, time=None)

Append a new node to the trajectory.

data()

Provides a dict containing the main characteristics.

duration()

Returns the trajectory time duration.

edges()

Returns a list of edges on which the particle moved.

The list may contain self loops (e.g. 3 → 3) if the particle was trapped in a node.

end_node()

Returns the ending node of the trajectory.

fpt(target)

Returns the first passage time through target.

start_node()

Returns the starting node of the trajectory.

time()

Returns the current trajectory time.

to_dataframe()

Represents the trajectory as DataFrame.

traps()

Returns a list of nodes in which the particle got trapped.

The list may contain multiple occurrences of the same node, meaning that the trapping happened multiple times.

Utilities

Algorithms and utilities for graphs.

er.graph.utils.k_cores(graph: networkx.classes.graph.Graph, k: int, inplace=False)

Return the components of the k-core graph.

Parameters

• graph (networkx.Graph) – An undirected graph.

• k (int) – The order of the core.

• inplace (bool) – If True, the k-core graph will be built directly by modifying the instance graph.

Returns

The core graph and a generator of its connected components.

Return type

(core_graph, connected_components)