Opened 5 years ago

Closed 4 years ago

# Effective Resistance for Graphs

Reported by: Owned by: afrancis gh-rajat1433 major sage-8.7 graph theory effective resistance, resitance distance, graphs, link prediction, sd90 Amanda Francis, Rajat Mittal David Coudert N/A 9648677

### Description

Calculate effective resistances between pairs of nodes in a graph.

### comment:1 Changed 5 years ago by afrancis

Branch: → u/afrancis/effective_resistance_for_graphs

### comment:2 Changed 5 years ago by git

Commit: → bc41ea18d585cffbe4311aa8c8a0a2fb80d85136

Branch pushed to git repo; I updated commit sha1. New commits:

 ​bc41ea1 Fixed some documentation errors

### comment:3 Changed 5 years ago by git

Commit: bc41ea18d585cffbe4311aa8c8a0a2fb80d85136 → 054b8ea360a9380b71477daf8778131bde50c15d

Branch pushed to git repo; I updated commit sha1. New commits:

 ​054b8ea Changed indentation authorship line

### comment:4 Changed 5 years ago by afrancis

Status: new → needs_review

### comment:5 Changed 5 years ago by dcoudert

Status: needs_review → needs_work

Welcome to Sagemath.

I have several comments on your ticket, some on the presentation and some on the algorithms you use.

Let's start with general comments, mostly on the presentation. I give them for the first method, but you should do the same for the other methods.

• effective_resistance(self,i,j) -> effective_resistance(self, i, j)
• Returns the effective resistance between nodes i and j -> Return the effective resistance between nodes i and j.
• Please add a description of the notion of effective resistance. What is it?
• You could add a link to the wikipedia page (e.g., in the seealso block). Should be See :wikipedia:Resistance_distance for more details
• Text lines (comments, definition, etc. must be in 80 columns format. Some code editors like emacs help you to do that without effort
• a straight linear 2-tree on 6 vertices. Well, I assume it's a Path graph of order 6, no?
• then you can use: G1 = graphs.PathGraph(6)
• replace G1 with G since you don't have G2
• in the test with the complete graph, you check only 1 edge. I assume you want to should that the resistance of each edge is 1/2, right? so you could do instead:
sage: G = graphs.CompleteGraph(4)
sage: all(G.effective_resistance(u, v) == 1/2 for u,v in G.edge_iterator(labels=0))
True

• Since I'm not familiar with this definition, it is not easy to tell which tests are important or not.
• Could you tell us what is the expected behavior if the graph has loops, multiple edges, is empty, is not connected ?

We will get to the algorithmic part latter. I need to understand the definition first. I have the feeling that we can do something faster, may be in another ticket.

### comment:6 Changed 5 years ago by git

Branch pushed to git repo; I updated commit sha1. New commits:

 ​391271a Documentation changes in response to ticket review

### comment:7 Changed 5 years ago by afrancis

a straight linear 2-tree on 6 vertices. Well, I assume it's a Path graph of order 6, no? then you can use: G1 = graphs.PathGraph?(6)

No, a straight linear 2-tree is like a ladder made out of triangles, not a path.

Since I'm not familiar with this definition, it is not easy to tell which tests are important or not. Could you tell us what is the expected behavior if the graph has loops, multiple edges, is empty, is not connected ?

Multiple edges should lower the effective resistance between pairs of nodes. A 'parallel' network transformation demonstrates how this works, but this is another method we are working on implementing at this Sagedays!

An empty graph has no node pairs, so an error should be returned for effective_resistance, and an empty matrix for effective_resistance_matrix.

I hadn't thought about connected graphs. Effective resistance between edges in different components should be infinity or return an error. I'll work on that. Also, loops should not be allowed. I'll fix that as well.

We will get to the algorithmic part latter. I need to understand the definition first. I have the feeling that we can do something faster, may be in another ticket.

Interesting, I would be happy to find out that this is true!

### comment:8 Changed 5 years ago by dcoudert

In the description of the method, use i instead of just i. This indicates that this is math code. It will be handled when generating the html documentation and so well displayed. You can also put latex equations if you like (e.g., \sqrt{x^3+1} \leq 2).

For wikipedia links, the _ in :wikipedia:Resistance_Distance is needed. If corresponds to the name of the page you see in the url https://en.wikipedia.org/wiki/Resistance_distance

When you have parameters with default value, don't put spaces. So def effective_resistance_matrix(self, nonedgesonly = True): -> def effective_resistance_matrix(self, nonedgesonly=True):. The same when you call the method.

if True eliminate pairs of adjacent vertices. Well, you don't eliminate pairs, you assign them value 0. It's different, no?

I prefer self.order() to self.num_verts().

For least_effective_resistance, you should rewrite like that (should be much faster).

    self._scream_if_not_simple()
if nonedgesonly and self.is_clique():
return []
S = self.effective_resistance_matrix(nonedgesonly=nonedgesonly)
if nonedgesonly:
edges = self.complement().edges(labels=0)
else:
edges = [(i,j) for i in range(n) for j in range(i+1,n)]
rmin = min(S[e] for e in edges)
return [e for e in edges if S[e] == rmin]


The self._scream_if_not_simple() will raise an error if the graph has loops or multiple edges. You don't need to add specific tests for that.

For effective_resistance(self, i, j):, you have to decide of what to do when i == j and you should check if not i in self or not j in self:.

The case of non connected should be treated at some point.

• method 1: if not in same component return +oo or 0. Otherwise, do computation only on that component
• method 2: you can certainly build the matrix from the results on each connected components
• method 3: You can do computations independently on each components and collect the result (faster than working on a big matrix)

### comment:9 Changed 5 years ago by dcoudert

you can also decide that the graph must be connected. I don't know what is best.

### comment:10 Changed 4 years ago by gh-rajat1433

According to wikipedia definition: In graph theory, the resistance distance between two vertices of a simple connected graph, G, is equal to the resistance between two equivalent points on an electrical network, constructed so as to correspond to G, with each edge being replaced by a 1 ohm resistance. It is a metric on graphs.

It assumes graph to be simple and connected, so I guess we can do the same here.

Can I work further on this ticket, if nobody else is working based on the proposed changes in the review above?

Last edited 4 years ago by gh-rajat1433 (previous) (diff)

Yes, you can.

### comment:12 Changed 4 years ago by gh-rajat1433

Owner: set to gh-rajat1433

### comment:13 Changed 4 years ago by gh-rajat1433

Branch: u/afrancis/effective_resistance_for_graphs → u/gh-rajat1433/24094_effective_resistance_for_graphs 391271aa1e1e2f506bff13dff21512832ad395bb sage-8.1 → sage-8.7

### comment:14 Changed 4 years ago by gh-rajat1433

I had a small doubt regarding should I be continue working on these functions in graph.py file or migrate them to generic_graph.py file. I guess these functions might be more suitable in latter module.

### comment:15 follow-up:  16 Changed 4 years ago by dcoudert

Is the method valid for both Graph and DiGraph ?

### comment:16 in reply to:  15 Changed 4 years ago by gh-rajat1433

Is the method valid for both Graph and DiGraph ?

It makes sense for Graph. Thanks for clearing the confusion.

### comment:17 Changed 4 years ago by git

Commit: → 8c4714cc21ffdc09682f69139dc0d26d1658f055

Branch pushed to git repo; I updated commit sha1. New commits:

 ​8c4714c Improved the resistance methods.

### comment:18 Changed 4 years ago by gh-rajat1433

Status: needs_work → needs_review

### comment:19 Changed 4 years ago by git

Commit: 8c4714cc21ffdc09682f69139dc0d26d1658f055 → e164fa3808c8bb5bd2225dd0085919f9fe486cbc

Branch pushed to git repo; I updated commit sha1. New commits:

 ​e164fa3 fixed bugs for documenting

### comment:20 Changed 4 years ago by gh-rajat1433

Reviewers: → David Coudert

I have pushed the modified code and passed all the tests and corner cases and also tested the documentation build.

### comment:21 Changed 4 years ago by git

Branch pushed to git repo; I updated commit sha1. New commits:

 ​37d171b fixed indentation and 80 column format

### comment:22 Changed 4 years ago by dcoudert

Status: needs_review → needs_work

Another round of comments. Certainly more to come :P The goal is to obtain the best possible code. It's always easier to read, so contains less errors and is way easier to maintain.

• Ensure that all comments are in 80 columns mode. For instace
-- Amanda Francis, Caitlin Lienkaemper, Kate Collins, Rajat Mittal (2019-03-10): methods for computing effective resistance
+- Amanda Francis, Caitlin Lienkaemper, Kate Collins, Rajat Mittal (2019-03-10):
+   methods for computing effective resistance

• You can use latex mode
-        OUTPUT: rational number denoting resistance between nodes i and j
+        OUTPUT: rational number denoting resistance between nodes i and j

• Although labels=0 is currently accepted, it is better to write labels=False
-            sage: all(G.effective_resistance(u, v) == 1/2 for u,v in G.edge_iterator(labels=0))
+            sage: all(G.effective_resistance(u, v) == 1/2 for u,v in G.edge_iterator(labels=False))

• not i in self: -> i not in self.
• some pep8 (I know it's impossible to be aware of all these rules. We try to do our best)
-            raise ValueError('The Graph is not a connected graph.')
+            raise ValueError('the Graph is not a connected graph')

• It is better to give the order of the vertices to laplacian_matrix. Furthermore, .vertices() currently sort vertices by default, but you don't need that. So use either list(self) or self.vertices(sort=False)
-        vert = self.vertices()
+        vert = list(self)
i1 = vert.index(i)
i2 = vert.index(j)
n = self.order()
-        L = self.laplacian_matrix()
+        L = self.laplacian_matrix(vertices=vert)

• -        sigma = matrix(Id[i1]-Id[i2])
-        diff = sigma* M * sigma.transpose()
+        sigma = matrix(Id[i1] - Id[i2])
+        diff = sigma * M * sigma.transpose()

• diff[0,0] -> diff[0, 0]
• Improve other methods the same way
• Add parameter vertices to least_effective_resistance

### comment:23 Changed 4 years ago by git

Branch pushed to git repo; I updated commit sha1. New commits:

 ​0cbfdbd fixed the coding style bugs

### comment:24 Changed 4 years ago by gh-rajat1433

Thanks for the review.

I don't think least_effective_resistance requires vertices as a perimeter as the user is generally interested in finding the least resistance wrt the whole graph. Still if it is required I can add that. Although I did add this

        verts = list(self)
verttoidx = {u: i for i, u in enumerate(verts)}
S = self.effective_resistance_matrix(vertices=verts, nonedgesonly=nonedgesonly)

Last edited 4 years ago by gh-rajat1433 (previous) (diff)

### comment:25 Changed 4 years ago by dcoudert

Right, I forgot the method returns vertices with least resistance.

This is not needed

-        verttoidx = {}


Also, please improve the code as much as you can according pep8 rules.

### comment:26 Changed 4 years ago by git

Commit: 0cbfdbd8a38ed67a7e1297da1c6a746c1a70bc33 → 5510cba70ba434f89e223a82e1cc47fc1ccb85ea

Branch pushed to git repo; I updated commit sha1. New commits:

 ​5510cba minor fix

### comment:27 Changed 4 years ago by gh-rajat1433

This is not needed

• verttoidx = {}

Yes I did that locally but forgot to commit :)

### comment:28 Changed 4 years ago by git

Commit: 5510cba70ba434f89e223a82e1cc47fc1ccb85ea → c8032e76acb6f6122f7a9b9d9ba05643357532b4

Branch pushed to git repo; I updated commit sha1. New commits:

 ​c8032e7 pep8 style

### comment:29 Changed 4 years ago by gh-rajat1433

Status: needs_work → needs_review

### comment:30 Changed 4 years ago by dcoudert

In method effective_resistance:

• I prefer this definition:
-        This is the resistance between two equivalent points of a simple connected graph
-        replacing each edge by a 1 ohm resistance.
+        The resistance distance between vertices i and j of a simple
+        connected graph G is defined as the effective resistance between the
+        two vertices on an electrical network constructed from G replacing
+        each edge of the graph by a unit (1 ohm) resistor.

• -              a similar method giving a matrix full of all effective resistances between all nodes
+              a similar method giving a matrix full of all effective
+              resistances between all nodes

• remove the '.' at the end of raise ValueError('the Graph is not a connected graph.')

In method effective_resistance_matrix

• add similar definition than above
• a ; is missing
-        - nonedgesonly -- boolean (default: True); if True assign
+        - nonedgesonly -- boolean (default: True) if True assign

• remove . at the end of raise ValueError('the Graph is not a connected graph.')
• -        S = d*onesvec.transpose() + onesvec*d.transpose() - 2* M
+        S = d * onesvec.transpose() + onesvec * d.transpose() - 2 * M


In least_effective_resistance

• add similar definition than above
• may be simpler message
-            raise ValueError('unable to compute least resistance for an empty Graph object')
+            raise ValueError('unable to compute least resistance on empty Graph')

• remove . at the end of raise ValueError('the Graph is not a connected graph.')
• -            edges = [(verts[i],verts[j]) for i in range(n) for j in range(i+1,n)]
+            edges = [(verts[i], verts[j]) for i in range(n) for j in range(i + 1, n)]


### comment:31 Changed 4 years ago by gh-rajat1433


-        S = d*onesvec.transpose() + onesvec*d.transpose() - 2* M
+        S = d * onesvec.transpose() + onesvec * d.transpose() - 2 * M



But according to pep8

Yes:

x = x*2 - 1

hypot2 = x*x + y*y

c = (a+b) * (a-b)

No:

x = x * 2 - 1

hypot2 = x * x + y * y

c = (a + b) * (a - b)

Am I missing something?

Version 1, edited 4 years ago by gh-rajat1433 (previous) (next) (diff)

### comment:32 Changed 4 years ago by git

Commit: c8032e76acb6f6122f7a9b9d9ba05643357532b4 → 4db2fdaeb65d5bf103db4da0b6b63306b728fda9

Branch pushed to git repo; I updated commit sha1. New commits:

 ​4db2fda fixed

### comment:33 Changed 4 years ago by dcoudert

• still missing ;
-        - nonedgesonly -- boolean (default: True) if True assign
+        - nonedgesonly -- boolean (default: True); if True assign

• Remove trailing white spaces. For instance the line above contains a useless space at the end
• instead of if n == 0:, we usually use if not n:
+        if i not in self:
+            raise ValueError("vertex ({0}) is not a vertex of the graph".format(repr(i)))
+        elif not j in self:


### comment:34 Changed 4 years ago by git

Commit: 4db2fdaeb65d5bf103db4da0b6b63306b728fda9 → 96486772b7f30f0171434050eb4a50c55a03c941

Branch pushed to git repo; I updated commit sha1. New commits:

 ​9648677 fixed

### comment:35 Changed 4 years ago by gh-rajat1433

I couldn't find a suitable way to unify

+        if i not in self:
+            raise ValueError("vertex ({0}) is not a vertex of the graph".format(repr(i)))
+        elif j not in self:


without printing the vertices values. If you have any suggestion I would like to know.

Even in the shortest path between u and v function

        if not self.has_vertex(u):
raise ValueError("vertex '{}' is not in the (di)graph".format(u))
if not self.has_vertex(v):
raise ValueError("vertex '{}' is not in the (di)graph".format(v))


this practice was followed.

### comment:36 Changed 4 years ago by dcoudert

it was just about the use of both forms: if i not in self: and if not j in self:. Now it's better.

### comment:37 Changed 4 years ago by dcoudert

Authors: Amanda Francis → Amanda Francis, Rajat Mittal needs_review → positive_review

For me this patch is not good to go.

### comment:38 Changed 4 years ago by gh-rajat1433

I guess you made a typo above regarding not good to go. (maybe?) :)

Last edited 4 years ago by gh-rajat1433 (previous) (diff)

### comment:39 Changed 4 years ago by dcoudert

Oups !

This patch is NOW good to go.

### comment:40 Changed 4 years ago by vbraun

Branch: u/gh-rajat1433/24094_effective_resistance_for_graphs → 96486772b7f30f0171434050eb4a50c55a03c941 → fixed positive_review → closed

### comment:41 Changed 5 months ago by slelievre

Commit: 96486772b7f30f0171434050eb4a50c55a03c941

Follow-up question at

Defaulting to nonedgesonly=False might have seemed more natural.

Since all examples and tests use False, why was True made the default?

### comment:42 Changed 5 months ago by dcoudert

May be it was useful for the original contributors ?

We can certainly change that, possibly with a deprecation for the change of default value.

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