DCSCSCI 2350 Social Economic Networks Graphs Reading Ch

DCS/CSCI 2350: Social & Economic Networks Graphs Reading: Ch 2 (Easley-Kleinberg) Mohammad T. Irfan Email: mirfan@bowdoin. edu

Graphs "Graph theory is a terminological jungle, in which any newcomer may plant a tree. " – John Barnes

Political blogs (2004)

Graphs Some Properties Puzzles: Degree-sum formula Max # of edges Konigsberg bridge problem

Konigsberg Bridge Problem

Graphs Paths Cycles

ARPANET (1970)

Graphs Connectivity Components

High school relationships (1993 -95)

Graphs Distance Breadth-First Search (BFS)

BFS algorithm Goal: calculate the distance from you to everyone else in a network Distance = shortest path length 1. Define distance from you to yourself = 0 2. Define distance from you to your friends = 1 3. Define distance from you to your friends-offriends (whose distances are undefined) = 2 4. Do not re-define the distance of any node! Continue this way until all reachable nodes' distances have been calculated. Distance to an unreachable node = infinity

BFS algorithm Resulting graph: BFS tree AKA "root" Other existing edges within a layer are not drawn here

When does BFS give shortest paths? When all the edges have the same "weight"/dist. Negative example: Frankfurt—Kassel—Munchen not shortest path

Reading Chapter 2 of Easley-Kleinberg Due before the next class