4.2. Friendship Paradox The degree distribution p, expresses the probability that a randomly selected node has k neighbors. However, if we randomly select a link, the probability that a node at one of its ends has degree k is q, = Akp, where A %3D is a normalization factor. (a) Find the normalization factor A, assuming that the network has
4.2. Friendship Paradox The degree distribution p, expresses the probability that a randomly selected node has k neighbors. However, if we randomly select a link, the probability that a node at one of its ends has degree k is q, = Akp, where A %3D is a normalization factor. (a) Find the normalization factor A, assuming that the network has
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Transcribed Image Text:4.2. Friendship Paradox
The degree distribution p, expresses the probability that a randomly
selected node has k neighbors. However, if we randomly select a link, the
probability that a node at one of its ends has degree k is q, = Akp, where A
is a normalization factor.
(a) Find the normalization factor A, assuming that the network has
a power law degree distribution with 2 < y < 3, with minimum
degree kin and maximum degree k
max'
(b) In the configuration model q, is also the probability that a ran-
domly chosen node has a neighbor with degree k. What is the av-
erage degree of the neighbors of a randomly chosen node?
(c) Calculate the average degree of the neighbors of a randomly cho-
sen node in a network with N = 104, y= 2.3, kmin=1 and k=1, 000.
%3D
%3D
%3D
max
Compare the result with the average degree of the network, (k).
(d) How can you explain the "paradox" of (c), that is a node's friends
have more friends than the node itself?
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