Ego-Networks

Analysis and Techniques

Ego-NetworksEgo is an individual focal node. Egos can be person, groups, organizations or whole societies and the nodes to whom, ego is directly connected to (these are called “alters”) plus ties, if any among alters.

Social Relations

Social Relations

Role Based

KINBrother ofFather of

Etc.

OtherFriend ofBoss of

Teachers of

Cognitive Affective

LikesKnows

Disperseadmires

Actions

TalksGives

Sells to

Characteristics of Ego Networks

• Homophily (i.e., "love of the same") is the tendency of individuals to associate and bond with similar others.

• The presence of homophily has been discovered in a vast array of network studies. For example: people have strongest ties with people who similar to themselves on key attributes, such as social calss, age sex, race, political views etc.

• Heterophily, or love of the different, is the tendency of individuals to collect in diverse groups; it is the opposite of Homophily.

• Heterophily is notable in successful organizations, where the resulting diversity of ideas is thought to promote an innovative environment. Recently it has become an area of social network analysis.

• Heterophily is particularly relevant for enterpreneurs.

• Granovetter believes that weak ties provide people with access to novel information.

Characteristics of Ego-Network

Homophily

Strong Ties

Transitivity

Cliques

Social Networks

Ego-Network and Related TerminologiesTransitivity: Transitivity in SNA is a property of ties. If there is a tie between ‘A’ and ‘B’ and one between ‘B’ and ‘C’ then in a transitive network ‘A’ and ‘C’ will also be connected.

Strong ties are more often transitive than weak ties.

Transitivity and Homophily together lead to the formation of Cliques.

Network density: A Network’s density is the ratio of the number of edges in the network over the

total number of possible edges between all pairs of nodes (which is 21nn where ‘n’ is the

number of vertices for an undirected graph).

Figure: Undirected Graph

In the example given above, the density of graph = 5/6=0.83 Note (Network density):

It is a common measure of how well connected a network is. A directed graph will have half the density of its undirected equivalent. Density is useful in comparing networks against each other.

Ego-Network and Related Terminologies: BridgesBridges: are nodes and edges that connect across groups (generally connecting two different communities).

Facilitates inter-group communication, increase social cohesion and help spur innovation. They are usually weak ties but not every weak tie is a bridge.

Another Definition: An edge is a bridge if its removal results in disconnection of its terminal nodes. Example:

Figure-1: E(2,5) is a Bridge

Figure-2: E(2,5) is not a bridge (why ?)

Relaxation in bridge technique

Relaxation in bridge technique: It is possible to relax the definition of bridge by checking if the distance between two terminal nodes increases if the edge is removed.

Note: the larger the distance, the weaker the tie is.

Figure: Undirected Graph

D(2,5)=4, if the E(2,5) is removed

D(5,6)=3, if the E(5,6) is removed

Neighborhood OverlapNeighborhood Overlap: Tie strength can be measured based on neighborhood overlap: the larger the overlap, the stronger the tie is:

ji

jiji VorVleastattoadjacentarewhofriendsofnumber

VandVbothoffriendssharedofnumberVVoverlap ,

2

,

ji

ji

NN

NN

ji VVoverlap

(-2) in the denominator is to exclude ji VandV

Figure: Undirected Graph

6,8,11,9,5,3,2,1

05,2 overlap

29,5,4,3,2,1

32,1

overlap

Visualizing or Analyzing your own Networks on facebook or Twitter using freely available tools

• Touch graph: you can visualize your network, examine friend ranks, friend’s position in the network, weak and strong ties and overall structure of your Ego-Network.

• Node XL: It imports data from Twitter, YouTube, Flicker and Your E-mail Client). Note: It can be downloaded from http://nodexl.codeplex.com/releases/view/40939

• Pajek (Windows, free).

• Netdraw (Windows, free).

• Mage (Windows, free).

• GUESS (all platforms, free and open source).

• R-Package for SNA (all platforms, free and open source).

References• Community Detection and Mining in Social Media.  Lei Tang and Huan Liu,

Morgan & Claypool, September, 2010.• C. C. Aggarwal (ed.), Social Network Data Analytics, DOI 10.1007/978-1-4419-

8462-3_1, Springer Science+Business Media, LLC 2011.• Linton Freeman, The Development of Social Network Analysis. Vancouver:

Empirical Press, 2006.