EXPLORAT

ORY SOCIA

L NETW

ORK ANALY

SIS

CH

AP

TE

R 4

: S

EN

TI M

EN

TS

& F

RI E

ND

SH

I P

• Cohesion of Affection• Attraction &

Repulsion• Factionalism

LIKE DISLIKE

BALANCE THEORY: 1940S, FRITZ HEIDER, SOCIAL PSYCHOLOGIST

Person (P)-Other(O)-Topic(X) TripleUnbalanced Balanced

Balancing:• Adjusting Opinion on X• Changing Affections for

O• Convincing O to X

SIGNED GRAPH

• D. Cartwright, Social Psychologist, & F. Harary, Mathematician • Friendship, Like, Attraction Positive ( + ) Weight Solid Arc• Hostility, Dislike, Repulsion Negative ( - ) Weight Dashed Arc

• Balanced [Directed] Signed Graph • No [semi] cycle with uneven number of negative arc• [semi] Cycle: Closed [semi] path, same start & end vertices

A signed graph is balanced if it can be partitioned into two clusters such that all positive ties are contained within the clusters and all

negative ties are situated between the clusters

SIGNED GRAPH

Technique [Small Graph]:Draws positive lines, which indicate attraction, as short as possible and negative lines, which signal repulsion, as long as possible, clusters of positive ties are clearly visible in a sociogram.

CLUSTERABILITY

• Generalize Balance Partitions to MORE than two

Davis proved that a network is clusterable if it contains no semicycles with exactly one negative arc. Clearly, balance is a special case of clusterability because all balanced semicycles are clusterable

PAJEK

1.Create the initial partition Number of partitions determines the number of clusters. manually/randomly by Partition > Create Random Partition.

2. Invoking the Balancing Optimization Technique Repetition number Alpha as the coefficient for error calculation Network > Signed Network > Create Partition > Doreian-Mrvarmethod*

Optimization Technique:• Several Solutions• Does not Find the Best Fitting Clustering• Starting Options may Yield Different Results

PAJEK

Forbidden Arcs Error : Maximally Balanced Minimized Error

LONGITUDINAL ANALYSIS

Error Evaluation of Network in Different Time Points