SNA Perspective of a Social Networking Website SOWT Reciprocity Multiplexity

							SNA Perspective of a Social Networking Website: SOWT, Reciprocity, Multiplexity and Exchange
Haris MEMIC Dzemal Bijedic University, Bosnia and Herzegovina memich@gmail.com

State of the Research
• Offline networks– much research • Online networks – some research
– Online communities
• Forum (bulleting board) • Blog • Wiki

Some research

– Social networking websites
• Specific kinds of Online communities Less research • “Social software applications”

State of the Research for OSN sites
• Online Social Networking websites
• Research based on traditional statistical approaches
– Common way of statistical analysis – Practical problems – computer resources

• Some applications of graph theory
– didn’t account for the sociology of connections and communication patterns

• SNA based research
– Very scarce – Needed … too be really able to better understand what goes on and why

This research
• Presents some of the preliminary results of an in depth analysis and modeling of relations and communication in the environment of an online social networking website by using methods and models of social network analysis. • Primary goal of the broader research (not presented here) is to compare networks of online learning students and regular students
– Suggestions are welcomed 

Goal 1
• • • Testing Strength of Weak Ties theory in the educational online social network (OSN) environment Friedkin-like tests (Friedkin, 1981) The tie between two persons was coded as strong if there is mutual, and weak if there is asymmetric friendship relationship between them. Hypothesis 1: Bridges and local bridges are disproportionately likely to be weak. Hypothesis 2: Average overlap of acquaintance (friendship) circles is greater for two persons tied by a strong tie, than for two persons tied by a weak tie, than for two persons that have no direct tie. Hypothesis 3: Probability of a tie is greatest if person i and person j are connected by a path of length two composed of strong ties, next greatest if i and j are connected by a path of length two composed of a strong tie and a weak tie, next greatest if i and j are connected by a path of length two composed of weak ties. If we can prove that the theory does hold, we could conclude that the online

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Goal 2
• Analysis of friendship and messages relations – Reciprocity of friendship relation – Reciprocity of messages relation – Multiplexity of friendship and messages – Exchange of friendship and messages • Biased net like measures of Skvoretz and Agneessens (2007)

Data & Setting
• • • • • • • Data was collected from an online social networking (OSN) website, from 29/12/2007 (beginning) to 23/06/2008 OSN is a semi-institutional website of the School of Informatics in Bosnia & Herzegovina. Out of 950 registered students (99% of entire student population), 771 were active (logged at least once after 15/02/2008) Students registered under real names ~ 1/4 of students are regular on-campus students, whereas ~ 3/4 are online learning students. The main purpose of OSN was to enhance social aspect of online learning students of the institution. OSN software was built on Elgg open-source SW, which author of the paper modified and extended heavily to accommodate it to requirements of its users and to be more competitive to its competitor site – an already existing online community site for students of this institution; anonymous.

Results
Basic network properties
Nr of actors Relation Density Reachability Average distance Diameter Friendship 0.0059 0.3413 3.5923 10 771 Messages 0.0026 0.2680 4.4028 10

Table: Basic network level structural properties for friendship and messages relations.

Results
SOWT: H1
Strong Weak Total Bridges & local bridges 129 283 412 Non-bridges 1015 937 1952 Total ties 1144 1220 2364

Table: Bridges / Local bridges by strength of tie. Density of an arbitrary tie in the network (counting symmetric links as single links) is 0.0080. Density of weak ties is 0.0041 (51.6% of all ties), density of strong ties is 0.0039 (48.4% of all ties) - a strong indication for reciprocity effect. Out of all bridges (and local bridges) 68.7% are weak ties. This is significantly larger than 51.6% (proportion of all ties that are weak). Significant Z-score (6.94) for the test that bridges are disproportionately

Results
SOWT: H2
Average proportion Strong Tie Weak Tie No Tie 0.1556 0.1080 0.0058 Number of Dyads 1144 1220 294471

Table: Average proportion of overlap of friendship circles.

Results
SOWT: H3
Strong 2-path Mixed 2-path Weak 2-path Network density Average proportion 0.1526 0.1119 0.1150 0.0059 Number of Dyads 8192 13284 8789

Table: Proportion of dyads tied by a strong, mixed or weak tie by type of connecting two-path. Significant Z-scores for test that probabilities of a tie in strong, mixed and weak 2-path dyads differs from chance (all > 110)

Results
Reciprocity of Friendships
Dyads Mutual Asymmetric Null Observed 1144 1220 294471 Expected 10.31 3487.37 293337.31 Difference 1134 -2267 1134

Table: Observed and expected number of MAN ‘friendship’ dyads, conditional on outdegree distribution Tau-value (biased net-like index for magnitude of bias toward friendship reciprocity) of 0.650 was obtained, variance of 10.19, Zscore of 355.16, p-value (2-sided test) of 0.0000 (rounded). -> Strong, significant tendency towards reciprocity.

Results
Reciprocity of Friendships 2
OSN website Tau-value Z-score 0.650 355.16 Lazega lawyers 0.563 28.17 Coleman high-school boys 0.489 / 0.437 24.99 / 22.36 MacRae prison friendships 0.416 19.58

Table: Comparison of biased net like reciprocity indexes of the OSN site with some of the well-known datasets.

Results
Reciprocity of Messages
The valued matrix for messages sent was dichotomized

Dyads Mutual Asymmetric Null

Observed 536 468 295831

Expected 1.99 1536.02 295296.99

Difference 534.01 -1068.02 534.01

Table: Observed and expected number of MAN ‘private messaging’ dyads, conditional on joint outdegree distribution. Tau-value for the reciprocity bias is 0.695, Z-score 379.61, p-value (2sided test) 0.0000 (rounded). -> Strong, significant tendency towards reciprocity of messaging

Results
Multiplexity of Friendships and Messages
Nr A,B ties Nr A, no B ties Nr no A, B ties Observed 542 2966 998 Expected 21.99 3486.01 1518.01 Difference 520 - 520 - 520

Nr no A, no B 589164 588643.99 520 ties Table: Tie-multiplexity census for friendship (A) and messages (B) relations, conditional on joint outdegree distribution. Biased net-like parameter for the magnitude of bies of tie-multiplexity is 0.525. Variance 20.91, Z-score 113.73. -> Statistically significant amount of multiplexity for friendship and messages relations.

Results
Exchange of Friendships and Messages
Observed Nr A,B ties Nr A, no B ties Nr no A, B ties 516 2992 1024 Expected 9.08 3498.92 1530.92 Difference 509.92 - 509.92 - 509.92

Nr no A, no B 589138 588631.08 509.92 ties Table 10: Biased Net Model for Exchange: Tie-exchange census for friendship (A) and messages(B), by fixing outdegree distribution. Eta-value for the magnitude of bias is 0.331. Variance 9.00, Z-score 168.93. -> Relatively significant amount of exchange between friendship and messages relations was found.

Summary, Conclusion, Further Research
• All of the proposed hypothesis for the test of SOWT theory were supported, except for the one related to the proportion of dyads tied by a strong, mixed or weak tie by type of connecting two-path.
– Further research on this subject is necessary. – Try to explain reasons for no full support of SOWT H3, by dividing network into two subnetworks

•

Strong, significant levels of reciprocity in both friendship and messages relations. Significant amount of multiplexity and relatively significant amount of exchange. The results presented indicate that friendship and communication networks in online social network are structured similarly as friendship networks in ‘real world’ off-line networks.
– Additional research and comparison with multiple datasets would be valuable in giving more value and generality to results that were presented here.

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Further Research (cont.)
• Compare networks and communication patterns of regular vs online learning students
– Find similarities and differences
• p-star modeling

– Longitudinal analysis (SIENA)

The End

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Reciprocity
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Multiplexity & Exchange
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