9282010 jure leskovec stanford cs224w social and

Info icon This preview shows pages 21–28. Sign up to view the full content.

View Full Document Right Arrow Icon
9/28/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 21
Image of page 21

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Measure of clustering (local structure i e (local structure, i.e., triangles in a graph) Clustering coefficient C of node i is: i k degree of node i i … degree of node Clustering coefficient: C = 1/n C C i =0 C i =1/3 C i =1 C = 1/n i 9/28/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 22
Image of page 22
1/n C i ient, C = 1 ng coeffic Clusterin Prob. of rewiring, p 9/28/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 23
Image of page 23

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Collaborations between actors (IMDB): 225,226 nodes, avg. degree k=61 Electrical power grid: 4 941 nodes k=2 67 4,941 nodes, k=2.67 Network of neurons 282 nodes, k=14 L ... Average shortest path length C ... Average clustering coefficient 9/28/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 24
Image of page 24
When we add one random connection out of each node we get short paths. Why? Suppose we build random edges by giving every node half edge and randomly pair them C id h h t t Consider a graph where we contract 2x2 subgraphs into supernodes Now we have 4 edges sticking out of each supernode From Thm. we have short paths between super nodes, we can turn this into a path in a real graph by dd h adding at most 2 steps per hop: O(2log n) 9/28/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 25
Image of page 25

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Ok so paths are short Ok, so paths are short And people are able to find them! (without the global knowledge of the network) 9/28/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 26
Image of page 26
s only knows locations of its friends s only knows locations of its friends and location of the target t s does not know links of anyone but itself Geographic navigation: s forwards the message to the node closest to t 9/28/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 27
Image of page 27

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Model: Grid where each node has one random edge This is a small world. Fact: A decentralized algorithm in Watts Strogatz model needs n 2/3 steps to reach t in expectation (even though paths of length log(n) exist). Proof: Let’s do this in 1 dim. n nodes on i l d di t d d a ring plus one random directed edge per node. Lower bound on search time is now n 1/2 d/d Lower bound for d dim.: n d/d+1 9/28/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 28
Image of page 28
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern