Struct net_ensembles::generic_graph::GenericGraph

pub struct GenericGraph<T: Node, A: AdjContainer<T>> { /* fields omitted */ }

Generic graph implementation

• contains multiple measurable quantities

Methods

impl<T: Node, A: AdjContainer<T>> GenericGraph<T, A>

pub fn new(size: u32) -> Self

Create new graph with size nodes and no edges

pub fn clear_edges(&mut self)

removes all edges from the graph

• inexpensive O(1), if there are no edges to begin with
• O(vertices) otherwise

pub fn sort_adj(&mut self)

Sort adjecency lists

If you depend on the order of the adjecency lists, you can sort them

Performance

• internally uses pattern-defeating quicksort as long as that is the standard
• sorts an adjecency list with length d in worst-case: O(d log(d))
• is called for each adjecency list, i.e., self.vertex_count() times

pub fn parse_str(to_parse: &str) -> Option<(&str, Self)>

parse from str

• tries to parse Graph from a str.
• will ignore leading whitespaces and other chars, as long as they do not match "next_id: "
• returns None if failed

Return

1. returns string slice beginning directly after the part, that was used to parse
2. the Graph resulting form the parsing

pub fn container(&self, index: usize) -> &A

get NodeContainer at index

• use this to iterate over neighbors
• use this to check, if vertices are adjacent

Warning

• panics if index out of bounds

pub fn container_iter(&self) -> Iter<A>

get iterator over NodeContainer in order of the indices

pub fn at(&self, index: usize) -> &T

For your calculations etc.

• read access to your struct T, stored at each vertex, that implements Node trait
• see first code example (beginning of this page)

pub fn at_mut(&mut self, index: usize) -> &mut T

For your calculations etc.

• write access to your struct T, stored at each vertex, that implements Node trait
• see first code example (beginning of this page)

pub fn vertex_count(&self) -> u32

returns number of vertices present in graph

pub fn average_degree(&self) -> f32

calculates the average degree of the graph

• (2 * edge_count) / vertex_count

pub fn add_edge(&mut self, index1: u32, index2: u32) -> Result<(), GraphErrors>

Adds edge between nodes index1 and index2

ErrorCases:

Error	Reason
GraphErrors::IndexOutOfRange	index1 or index2 larger than self.vertex_count()
GraphErrors::EdgeExists	requested edge already exists!

panics

• if indices out of bounds
• in debug: If index0 == index1

pub fn remove_edge(
    &mut self,
    index1: u32,
    index2: u32
) -> Result<(), GraphErrors>

Removes edge between nodes index1 and index2

ErrorCases:

Error	Reason
GraphErrors::IndexOutOfRange	index1 or index2 larger than self.vertex_count()
GraphErrors::EdgeDoesNotExist	requested edge does not exists

panics

• if index out of bounds
• in debug: If index0 == index1

pub fn edge_count(&self) -> u32

returns total number of edges in graph

pub fn degree(&self, index: usize) -> Option<usize>

returns number of vertices adjacent to vertex index

pub fn dfs(&self, index: u32) -> Dfs<T, A>

returns Iterator

• the iterator will iterate over the vertices in depth first search order, beginning with vertex index.
• iterator returns node

Order

Order is guaranteed to be in DFS order, however if this order is not unambigouse adding edges and especially removing edges will shuffle the order.

Note:

Will only iterate over vertices within the connected component that contains vertex index

pub fn dfs_with_index(&self, index: u32) -> DfsWithIndex<T, A>

returns Iterator

• the iterator will iterate over the vertices in depth first search order, beginning with vertex index.
• Iterator returns tuple (index, node)

Order

Order is guaranteed to be in DFS order, however if this order is not unambigouse adding edges and especially removing edges will shuffle the order.

Note:

Will only iterate over vertices within the connected component that contains vertex index

pub fn bfs_index_depth(&self, index: u32) -> Bfs<T, A>

returns Iterator

• the iterator will iterate over the vertices in breadth first search order, beginning with vertex index.
• Iterator returns tuple (index, node, depth)

depth

• starts at 0 (i.e. the first element in the iterator will have depth = 0)
• depth equals number of edges in the shortest path from the current vertex to the first vertex (i.e. to the vertex with index index)

Order

Order is guaranteed to be in BFS order, however if this order is not unambigouse adding edges and especially removing edges will shuffle the order.

Note:

Will only iterate over vertices within the connected component that contains vertex index

pub fn is_connected(&self) -> Option<bool>

result	condition
None	if graph does not contain any vertices
Some(true)	else if all vertices are connected by paths of edges
Some(false)	otherwise

pub fn q_core(&self, q: u32) -> Option<u32>

definition

Calculates the size of the q-core (i.e. number of nodes in the biggest possible set of nodes, where all nodes from the set are connected with at least q other nodes from the set)

returns None if impossible to calculate (e.g. vertex_count == 0 or q <= 1)

Example

use net_ensembles::EmptyNode;
use net_ensembles::Graph;

let graph: Graph<EmptyNode> = Graph::new(0);
assert_eq!(graph.q_core(1), None);
assert_eq!(graph.q_core(2), None);

let graph2: Graph<EmptyNode> = Graph::new(1);

assert_eq!(graph2.q_core(1), None);
assert_eq!(graph2.q_core(2), Some(0));


// create complete graph
let mut graph3: Graph<EmptyNode> = Graph::new(20);
for i in 0..graph3.vertex_count() {
    for j in i+1..graph3.vertex_count() {
        graph3.add_edge(i, j).unwrap();
    }
}

// since this is a complete graph, the q-core should always consist of 20 nodes
// as long as q < 20, as every node has 19 neighbors
for i in 2..20 {
    assert_eq!(graph3.q_core(i), Some(20));
}
assert_eq!(graph3.q_core(20), Some(0));

pub fn connected_components(&self) -> Vec<u32>

compute sizes of all connected components

• the number of connected components is the size of the returned vector, i.e. result.len()
• returns empty vector, if graph does not contain vertices
• returns (reverse) ordered vector of sizes of the connected components, i.e. the biggest component is of size result[0] and the smallest is of size result[result.len() - 1]

pub fn leaf_count(&self) -> usize

Count number of leaves in the graph, i.e. vertices with exactly one neighbor

pub fn to_dot(&self) -> String

• Creates String which contains the topology of the network in a format that can be used by circo etc. to generate a pdf of the graph.
• indices are used as labels
• search for graphviz to learn about .dot format

pub fn to_dot_with_labels_from_contained<F>(
    &self,
    dot_options: &str,
    f: F
) -> String where
    F: Fn(&T, usize) -> String, 

Example

use std::fs::File;
use std::io::prelude::*;
use net_ensembles::{Graph, EmptyNode, dot_constants::EXAMPLE_DOT_OPTIONS};

let mut graph: Graph<EmptyNode> = Graph::new(3);
graph.add_edge(0, 1).unwrap();
graph.add_edge(0, 2).unwrap();
graph.add_edge(1, 2).unwrap();

// create string of dotfile
let s = graph.to_dot_with_labels_from_contained(
   EXAMPLE_DOT_OPTIONS,
   |_contained, index| format!("Hey {}!", index)
);

// write to file
let mut f = File::create("example.dot").expect("Unable to create file");
f.write_all(s.as_bytes()).expect("Unable to write data");

In this example, example.dot now contains:

graph G{
    bgcolor="transparent";
    fontsize=50;
    node [shape=ellipse, penwidth=1, fontname="Courier", pin=true ];
    splines=true;
    0 1 2 ;
    "0" [label="Hey 0!"];
    "1" [label="Hey 1!"];
    "2" [label="Hey 2!"];
    0 -- 1
    0 -- 2
    1 -- 2
}

Then you can use, e.g.,

foo@bar:~$ circo example.dot -Tpdf > example.pdf

to create a pdf representation from it. Search for graphviz to learn more.

pub fn to_dot_with_labels_from_container<F>(
    &self,
    dot_options: &str,
    f: F
) -> String where
    F: Fn(&A, usize) -> String, 

Same as to_dot_with_labels_from_contained but with access to neighbor information

Example

use std::fs::File;
use std::io::prelude::*;
use net_ensembles::traits::*;
use net_ensembles::dot_constants::*;
use net_ensembles::{Graph,EmptyNode};

let mut graph: Graph<EmptyNode> = Graph::new(5);
graph.add_edge(0, 1).unwrap();
graph.add_edge(0, 2).unwrap();
graph.add_edge(1, 2).unwrap();
graph.add_edge(0, 3).unwrap();
graph.add_edge(3, 4).unwrap();

// create string of dotfile
let s = graph.to_dot_with_labels_from_container(
    &[SPLINES, NO_OVERLAP].join("\n\t"),
    |container, index|
    {
        container.contained();  // does nothing in this example, but you can still access
                                // contained, as you could in
                                // to_dot_with_labels_from_contained
        format!("index {}, degree: {}", index, container.degree())
    }
);

// write to file
let mut f = File::create("example_2.dot").expect("Unable to create file");
f.write_all(s.as_bytes()).expect("Unable to write data");

In this example, example_2.dot now contains:

graph G{
	splines=true;
	overlap=false;
	0 1 2 3 4 ;
	"0" [label="index 0, degree: 3"];
	"1" [label="index 1, degree: 2"];
	"2" [label="index 2, degree: 2"];
	"3" [label="index 3, degree: 2"];
	"4" [label="index 4, degree: 1"];
	0 -- 1
	0 -- 2
	0 -- 3
	1 -- 2
	3 -- 4
}

Then you can use, e.g.,

foo@bar:~$ circo example_2.dot -Tpdf > example_2.pdf

to create a pdf representation from it. Search for graphviz to learn more.

pub fn diameter(&self) -> Option<u32>

• returns None if graph not connected or does not contain any vertices
• uses repeated breadth first search

pub fn longest_shortest_path_from_index(&self, index: u32) -> Option<u32>

calculate the size of the longest shortest path starting from vertex with index index using breadth first search

pub fn vertex_biconnected_components(
    self,
    alternative_definition: bool
) -> Vec<usize>

calculate sizes of all binode connected components

• returns (reverse) ordered vector of sizes i.e. the biggest component is of size result[0] and the smallest is of size result[result.len() - 1]
• destroys the underlying topology and therefore moves self
• if you still need your graph, use self.clone().vertex_biconnected_components(false/true) for your calculations

Definition: vertex_biconnected_components(false)

Here, the (vertex) biconnected component of a graph is defined as maximal subset of nodes, where any one node could be removed and the remaining nodes would still be a connected component.

Note

Two vertices connected by an edge are considered to be biconnected, since after the removal of one vertex (and the corresponding edge), only one vertex remains. This vertex is in a connected component with itself.

Alternative Definition: vertex_biconnected_components(true)

If you want to use the alternative definition:

The biconnected component is defined as maximal subset of vertices, where each vertex can be reached by at least two node independent paths

The alternative definition just removes all 2s from the result vector.

Citations

I used the algorithm described in this paper:

J. Hobcroft and R. Tarjan, "Algorithm 447: Efficient Algorithms for Graph Manipulation" Commun. ACM, 16:372-378, 1973, DOI: 10.1145/362248.362272

You can also take a look at:

M. E. J. Newman, "Networks: an Introduction" Oxfort University Press, 2010, ISBN: 978-0-19-920665-0.

pub fn vertex_load(&self, include_endpoints: bool) -> Vec<f64>

Closely related (most of the time equal) to betweeness

calculates vertex_load of all vertices in O(edges * vertices)

• calculates the vertex_load for every vertex
• defined as how many shortest paths pass through each vertex

variant
vertex_load(true)	includes endpoints in calculation (for a complete graph with N vertices, every node will have vertex_load N - 1)
vertex_load(false)	excludes endpoints in calculation (for a complete graph with N vertices, every node will have vertex_load 0)

Citations

I used the algorithm described in

M. E. J. Newman, "Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality", Phys. Rev. E 64, 016132, 2001, DOI: 10.1103/PhysRevE.64.016132

see also:

M. E. J. Newman, "Erratum: Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality", Phys. Rev. E 73, 039906, 2006, DOI: 10.1103/PhysRevE.73.039906

pub fn transitivity(&self) -> f64

Calculates transitivity of graph

• related to cluster coefficient (Note: transitivity and cluster coefficient are similar, but not necessarily equal)
• returns NaN, if there are no paths of length two in the graph

Definition

transitivity = (number of closed paths of length two) / (number of paths of length two)

Citations

For the definition see for example:

M. E. J. Newman, "Networks: an Introduction" Oxfort University Press, 2010, ISBN: 978-0-19-920665-0.

impl<T: Node> GenericGraph<T, SwContainer<T>>

pub fn reset_edge(&mut self, index0: u32, index1: u32) -> SwChangeState

Reset small-world edge to its root state

• panics if index out of bounds
• in debug: panics if index0 == index1

pub fn rewire_edge(
    &mut self,
    index0: u32,
    index1: u32,
    index2: u32
) -> SwChangeState

Rewire edges

• rewire edge (index0, index1) to (index0, index2)

panics

• if indices are out of bounds
• in debug: panics if index0 == index2
• edge (index0, index1) has to be rooted at index0, else will panic in debug mode

Trait Implementations

impl<T: Clone + Node, A: Clone + AdjContainer<T>> Clone for GenericGraph<T, A>

fn clone(&self) -> GenericGraph<T, A>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Debug + Node, A: Debug + AdjContainer<T>> Debug for GenericGraph<T, A>

fn fmt(&self, f: &mut Formatter) -> Result

Formats the value using the given formatter.

impl<T: Node, A: AdjContainer<T>> Display for GenericGraph<T, A>

fn fmt(&self, f: &mut Formatter) -> Result

Formats the value using the given formatter.