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Unformatted text preview: availability of computers and computer networks that
allow us to gather and analyze large scale data. New Analytical Approach:
Find statistical properties that characterize the structure of these
networks and ways to measure them
Create models of networks
Predict behavior of networks on the basis of measured structural
properties and models
5 Networks: Lecture 2 Graphs Graphs—1
We represent a network by a graph (N , g ), which consists of a set of nodes
N = {1, . . . , n } and an n × n matrix g = [gij ]i ,j ∈N (referred to as an
adjacency matrix), where gij ∈ {0, 1} represents the availability of an edge
from node i to node j .
The edge weight gij > 0 can also take on nonbinary values,
representing the intensity of the interaction, in which case we refer to
(N , g ) as a weighted graph.
We refer to a graph as a directed graph (or digraph) if gij �= gji and an
undirected graph if gij = gji for all i , j ∈ N .
1
⎡
0
Example 1: ⎣ 0
1 1
0
0 ⎤
0 1 ⎦ ⇒
0
2 3 1
⎡
0
Example 2: ⎣ 1
1 1
0
1 1 ⎤
1
1 ⎦⇒
0 ⇒
2 3 2 3
6 Networks: Lecture 2 Graphs Graphs—2
Another representation of a graph is given by (N , E ), where E is the
set of...
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 Fall '09
 Acemoglu

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