How to find connected components of a random graph?
Let’s learn how to find connected components of a random graph. The most accurate or helpful solution is served by Mathematics.
There are ten answers to this question.
Best solution
Let $n$ and $k$ be integers with $1\le k < n$. Form a graph $G$ whose vertices are the integers $0,1,2,...,n-1$. We have an edge joining the vertices $a$ and $b$ provided $$a-b \equiv \pm k \pmod n\;.$$ We were given the example if $n=20$ and $k=6$, then vertex $2$ would be adjacent to vertices $8$ and $16$. I need to find a formula involving $n$ and $k$ for the number of connected components of $G$. I tried creating other examples, with $k=1$ and $n=2$, with $k=2$ and $n=20$, etc, and the pattern...
Answer:
Start at vertex $0$; it's adjacent to $k\bmod n$. From there you can go to $2k\bmod n$, then to $3k...
Ali at Mathematics Mark as irrelevant Undo
Other solutions
Hey guys, I need to find connected components for a huge dataset. (Graph being Undirected). One obvious choice is MapReduce. But i'm a newbie to MapReduce and am quiet short of time to pick it up and to code it myself. I was just wondering if there is...
Answer:
I know very little about graph algorithms, but I do know a little about map reduce. I think graph algorithms...
Earl Hathaway at Quora Mark as irrelevant Undo
A g-square graph of a given connected undirected graph 'g' is defined as the given graph g + we need to add an edge between any pair of vertices of g whose distance between them is exactly 2.
Answer:
This is just my analysis after taking a first look at the question, I do not know the correct solution...
Aniket Alshi at Quora Mark as irrelevant Undo
Draw each of the following vectors on graph paper, then find the x- and y- components. Make sure to include units in your answers for the components. a) ⃑r = (65 m, 30degrees above ...show more
Answer:
a) r= (65cos30i + 65sin30j)m b) v=( -125cos40i -125sin40j)m/s c) not sure if im visualizing this one...
IKCRDE5DXZEA2K4QXEWOFKORVE at Yahoo! Answers Mark as irrelevant Undo
I want to carry out Graph Clustering in a huge undirected graph with millions of edges and nodes. Graph is almost clustered with different clusters joined together only by some nodes(kind of ambiguous nodes which can relate to multiple clusters). There...
Answer:
Got this answer on Stackoverflow[1] .... analysing networks with millions of nodes Seems legit, in...
Shashank Gupta at Quora Mark as irrelevant Undo
I have been reading about spectral graph theory from Daniel A. Spielman's notes. Fiedler’s Nodal Domain Theorem from ( http://www.cs.yale.edu/homes/spielman/561/2009/lect02-09.pdf ) says that : Let [math]G = (V, E, w)[/math] be a weighted...
Answer:
What are 'values' of eigenvectors? That's really a vague entity to define, as eigenvectors are not unique...
Shyama Purnima at Quora Mark as irrelevant Undo
I need help to understand how to come up with a solution for this problem. Appreciate any help! A graph has n vertices and m edges. How many connected components that graph can have at most? How man connected components the graph can hav at least?
Answer:
I'll comeback later if I recall some math. However I would look through some combinatorics book. My...
Murad A at Yahoo! Answers Mark as irrelevant Undo
I ran pagerank on a large graph. But, the graph is disjoint connected components. I have noticed that nodes in a small component received relatively high score, even though the number of nodes in the component is much smaller. Is this a disadvantage...
Answer:
PageRank "fixes" this with the "teleportation" parameter, famously set to 0.15,...
Jay Kreps at Quora Mark as irrelevant Undo
Ive decided to build an HTPC/downstairs computer an i need someone with experience to check that all the components i have found will work. Im on a relativly low budget so i have tried to find some cheap but good components. My criteria for the PC is...
Answer:
Okay, here we go. Your motherboard choice is fine - I found a fairly decent review on it. That will...
Rhyled at Yahoo! Answers Mark as irrelevant Undo
What is the most efficient algorithm to decompose a Strongly Connected Component of a directed graph into ALL of the constituent cycles? I solved this in a brute-force manner (Do DFS within the SCC from "every" vertex, find cycles by detecting...
Answer:
D. B. Johnson, "Finding All the Elementary Circuits of a Directed Graph," SIAM Journal of...
Abhijeet N. Vaidya at Quora Mark as irrelevant Undo
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