Social Media Mining: An Introduction

P1: qVa Trim: 6.125in×9.25in Top: 0.5in Gutter: 0.75in
CUUS2079-07 CUUS2079-Zafarani 978 1 107 01885 3 January 13, 2014 17:17

7.2 Information Cascades 187

are connected by a network and (2) individuals are only observing decisions

of their immediate neighbors (friends). Therefore, cascade users have less

information available to them compared to herding users, where almost all

information about decisions are available.

There are many approaches to modeling information cascades. Next, we

introduce a basic model that can help explain information cascades.

7.2.1 Independent Cascade Model (ICM)

In this section, we discuss the independent cascade model (ICM) [Kempe

et al., 2003] that can be utilized to model information cascades. Variants

of this model have been discussed in the literature. Here, we discuss the

one detailed byKempe et al. [2003]. Interested readers can refer to the

bibliographic notes for further references. Underlying assumptions for this

model include the following:

 The network is represented using a directed graph. Nodes are actors

and edges depict the communication channels between them. A node

can only influence nodes that it is connected to.

 Decisions are binary – nodes can be eitheractiveorinactive. An active

nodes means that the node decided to adopt the behavior, innovation,

or decision.

 A node, once activated, can activate its neighboring nodes.

 Activation is aprogressiveprocess, where nodes change from inactive

to active, but not vice versa.^1

Considering nodes that are active as senders and nodes that are being

activated as receivers, in the independent cascade model (ICM) senders

activate receivers. Therefore, ICM is denoted as asender-centricmodel. In SENDER-

CENTRIC

MODEL

this model, the node that becomes active at timethas, in the next time step

t+1, one chance of activating each of its neighbors. Letvbe an active

node at timet. Then, for any neighborw, there is a probabilitypv,wthat

nodewgets activated att+1. A nodevthat has been activated at timet

has a single chance of activating its neighborwand that activation can only

happen att+1. We start with a set of active nodes and we continue until

no further activation is possible. Algorithm7.1details the process of the

ICM model.

Example 7.2.Consider the network in Figure7.4as an example. The

network is undirected; therefore, we assume pv,w=pw,v. Since it is