This document defines and describes social networks. It states that a social network consists of: 1) A collection of entities that participate in the network, typically people. 2) At least one relationship between the entities in the network, which can be discrete (e.g. friends) or have a degree. 3) An assumption of non-randomness where entities related to one entity are more likely to be related to each other. Social networks can be modeled as graphs with entities as nodes and relationships as edges between nodes, which may be directed or undirected.

1. What isa Social Network?
Whenwe thinkof a social network,we thinkof Facebook,Twitter,Google+,
or anotherwebsite thatiscalleda“social network,”andindeedthiskindof
networkisrepresentativeof the broaderclassof networkscalled“social.” The
essential characteristicsof asocial networkare:
1. There is a collectionof entitiesthatparticipate inthe network.Typically,
these entitiesare people,buttheycouldbe somethingelseentirely.We
shall discusssome otherexamplesinSection10.1.3.
2. There is at leastone relationshipbetweenentitiesof the network.On
Facebookor itsilk,thisrelationshipiscalledfriends.Sometimesthe
relationshipisall-or-nothing;twopeople are eitherfriendsortheyare
not.However,inotherexamplesof social networks,the relationshiphasa
degree.Thisdegree couldbe discrete;e.g.,friends,family,acquaintances,
or none as inGoogle+.It couldbe a real number;anexample would
be the fractionof the average day thattwo people spendtalkingto each
other.
3. There is an assumptionof nonrandomnessorlocality.Thisconditionis
the hardestto formalize,butthe intuitionisthatrelationshipstendto
cluster.Thatis, if entityA isrelatedtoboth B and C,thenthere isa
higherprobabilitythanaverage thatB and C are related.
10.1.2 Social NetworksasGraphs
Social networksare naturallymodeledasgraphs,whichwe sometimesreferto
as a social graph. The entitiesare the nodes,andanedge connectstwonodes
if the nodesare relatedbythe relationshipthatcharacterizesthe network.If
there isa degree associatedwiththe relationship,thisdegree isrepresentedby
labelingthe edges.Often,social graphsare undirected,asforthe Facebook
friendsgraph.Buttheycan be directedgraphs, asforexample the graphsof
followersonTwitterorGoogle+.
The Barabási–Albert model is one of several proposed models that generate scale-free
networks. It incorporates two important general concepts: growth and preferential
attachment. Both growth and preferential attachment exist widely in real networks. Growth
means that the number of nodes in the network increases over time.
Preferential attachment means that the more connected a node is, the more likely it is to

2. receive new links. Nodes with higher degree have stronger ability to grab links added to the
network.