STANDARD NETWORK ANALYSIS REPORT

STANDARD NETWORK ANALYSIS REPORT

Input data: s50_d02 - 1

Start time: Fri Oct 14 13:33:21 2011

Data Description

Calculates common social network measures on each selected input network.

Network network

Network Level Measures

MeasureValue
Row count50.000
Column count50.000
Link count116.000
Density0.047
Components of 1 node (isolates)2
Components of 2 nodes (dyadic isolates)0
Components of 3 or more nodes1
Reciprocity0.432
Characteristic path length4.490
Clustering coefficient0.310
Network levels (diameter)13.000
Network fragmentation0.079
Krackhardt connectedness0.921
Krackhardt efficiency0.969
Krackhardt hierarchy0.740
Krackhardt upperboundedness0.867
Degree centralization0.046
Betweenness centralization0.123
Closeness centralization0.092
Eigenvector centralization0.420
Reciprocal (symmetric)?No (43% of the links are reciprocal)

Node Level Measures

MeasureMinMaxAvgStddev
Total degree centrality0.0000.0920.0470.024
Total degree centrality [Unscaled]0.0009.0004.6402.330
In-degree centrality0.0000.1220.0470.031
In-degree centrality [Unscaled]0.0006.0002.3201.529
Out-degree centrality0.0000.1020.0470.026
Out-degree centrality [Unscaled]0.0005.0002.3201.272
Eigenvector centrality0.0000.5300.1270.155
Eigenvector centrality [Unscaled]0.0000.3750.0900.109
Eigenvector centrality per component0.0000.3600.0860.105
Closeness centrality0.0200.0820.0380.022
Closeness centrality [Unscaled]0.0000.0020.0010.000
In-Closeness centrality0.0200.0510.0330.011
In-Closeness centrality [Unscaled]0.0000.0010.0010.000
Betweenness centrality0.0000.1470.0260.038
Betweenness centrality [Unscaled]0.000346.00061.56090.013
Hub centrality0.0000.7070.1150.164
Authority centrality0.0000.7570.1040.171
Clique membership count0.0004.0001.2000.917
Simmelian ties0.0000.0610.0120.021
Simmelian ties [Unscaled]0.0003.0000.6001.039
Clustering coefficient0.0001.0000.3100.316

Key Nodes

This chart shows the Source nodes that is repeatedly top-ranked in the measures listed below. The value shown is the percentage of measures for which the Source nodes was ranked in the top three.

Total degree centrality

The Total Degree Centrality of a node is the normalized sum of its row and column degrees. Individuals or organizations who are "in the know" are those who are linked to many others and so, by virtue of their position have access to the ideas, thoughts, beliefs of many others. Individuals who are "in the know" are identified by degree centrality in the relevant social network. Those who are ranked high on this metrics have more connections to others in the same network. The scientific name of this measure is total degree centrality and it is calculated on the agent by agent matrices.

Input network: network (size: 50, density: 0.0473469)

RankSource nodesValueUnscaledContext*
1170.0929.0001.481
2300.0929.0001.481
3460.0929.0001.481
4100.0828.0001.142
5190.0828.0001.142
6260.0828.0001.142
7110.0717.0000.802
8360.0717.0000.802
9370.0717.0000.802
10400.0717.0000.802

* Number of standard deviations from the mean of a random network of the same size and density

Mean: 0.047Mean in random network: 0.047
Std.dev: 0.024Std.dev in random network: 0.030

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In-degree centrality

The In Degree Centrality of a node is its normalized in-degree. For any node, e.g. an individual or a resource, the in-links are the connections that the node of interest receives from other nodes. For example, imagine an agent by knowledge matrix then the number of in-links a piece of knowledge has is the number of agents that are connected to. The scientific name of this measure is in-degree and it is calculated on the agent by agent matrices.

Input network(s): network

RankSource nodesValueUnscaled
1300.1226.000
2190.1025.000
3260.1025.000
4460.1025.000
540.0824.000
6100.0824.000
7150.0824.000
8170.0824.000
9280.0824.000
10320.0824.000

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Out-degree centrality

For any node, e.g. an individual or a resource, the out-links are the connections that the node of interest sends to other nodes. For example, imagine an agent by knowledge matrix then the number of out-links an agent would have is the number of pieces of knowledge it is connected to. The scientific name of this measure is out-degree and it is calculated on the agent by agent matrices. Individuals or organizations who are high in most knowledge have more expertise or are associated with more types of knowledge than are others. If no sub-network connecting agents to knowledge exists, then this measure will not be calculated. The scientific name of this measure is out degree centrality and it is calculated on agent by knowledge matrices. Individuals or organizations who are high in "most resources" have more resources or are associated with more types of resources than are others. If no sub-network connecting agents to resources exists, then this measure will not be calculated. The scientific name of this measure is out degree centrality and it is calculated on agent by resource matrices.

Input network(s): network

RankSource nodesValueUnscaled
1110.1025.000
2170.1025.000
3370.1025.000
4100.0824.000
5120.0824.000
6250.0824.000
7360.0824.000
8460.0824.000
910.0613.000
10140.0613.000

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Eigenvector centrality

Calculates the principal eigenvector of the network. A node is central to the extent that its neighbors are central. Leaders of strong cliques are individuals who or organizations who are collected to others that are themselves highly connected to each other. In other words, if you have a clique then the individual most connected to others in the clique and other cliques, is the leader of the clique. Individuals or organizations who are connected to many otherwise isolated individuals or organizations will have a much lower score in this measure then those that are connected to groups that have many connections themselves. The scientific name of this measure is eigenvector centrality and it is calculated on agent by agent matrices.

Input network: network (size: 50, density: 0.0473469)

RankSource nodesValueUnscaledContext*
1300.5300.3750.399
2110.5080.3590.317
3190.4680.3310.170
4360.4090.289-0.050
5410.3590.254-0.233
6260.3310.234-0.336
7330.3260.231-0.355
810.3220.228-0.371
9100.3220.228-0.371
10420.3020.214-0.444

* Number of standard deviations from the mean of a random network of the same size and density

Mean: 0.127Mean in random network: 0.422
Std.dev: 0.155Std.dev in random network: 0.270

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Eigenvector centrality per component

Calculates the principal eigenvector of the network. A node is central to the extent that its neighbors are central. Each component is extracted as a separate network, Eigenvector Centrality is computed on it and scaled according to the component size. The scores are then combined into a single result vector.

Input network(s): network

RankSource nodesValue
1300.360
2110.345
3190.318
4360.277
5410.244
6260.225
7330.222
810.219
9100.219
10420.205

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Closeness centrality

The average closeness of a node to the other nodes in a network (also called out-closeness). Loosely, Closeness is the inverse of the average distance in the network from the node to all other nodes.

Input network: network (size: 50, density: 0.0473469)

RankSource nodesValueUnscaledContext*
1370.0820.002-2.241
2250.0820.002-2.255
3210.0810.002-2.286
4310.0780.002-2.405
5320.0780.002-2.405
6170.0770.002-2.433
7240.0730.001-2.561
8270.0730.001-2.564
950.0730.001-2.568
10220.0720.001-2.578

* Number of standard deviations from the mean of a random network of the same size and density

Mean: 0.038Mean in random network: 0.150
Std.dev: 0.022Std.dev in random network: 0.030

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In-Closeness centrality

The average closeness of a node from the other nodes in a network. Loosely, Closeness is the inverse of the average distance in the network to the node and from all other nodes.

Input network(s): network

RankSource nodesValueUnscaled
1190.0510.001
2300.0510.001
3360.0510.001
4410.0510.001
5150.0500.001
6290.0490.001
770.0490.001
8420.0490.001
9380.0490.001
10260.0480.001

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Betweenness centrality

The Betweenness Centrality of node v in a network is defined as: across all node pairs that have a shortest path containing v, the percentage that pass through v. Individuals or organizations that are potentially influential are positioned to broker connections between groups and to bring to bear the influence of one group on another or serve as a gatekeeper between groups. This agent occurs on many of the shortest paths between other agents. The scientific name of this measure is betweenness centrality and it is calculated on agent by agent matrices.

Input network: network (size: 50, density: 0.0473469)

RankSource nodesValueUnscaledContext*
1370.147346.0000.394
2320.116273.0000.269
3210.112264.0000.253
4170.110258.5000.244
5300.107252.6670.234
6190.101237.7500.208
7290.096225.5830.187
8330.052121.5830.009
9360.050117.5830.002
10280.04298.500-0.031

* Number of standard deviations from the mean of a random network of the same size and density

Mean: 0.026Mean in random network: 0.050
Std.dev: 0.038Std.dev in random network: 0.247

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Hub centrality

A node is hub-central to the extent that its out-links are to nodes that have many in-links. Individuals or organizations that act as hubs are sending information to a wide range of others each of whom has many others reporting to them. Technically, an agent is hub-central if its out-links are to agents that have many other agents sending links to them. The scientific name of this measure is hub centrality and it is calculated on agent by agent matrices.

Input network(s): network

RankSource nodesValue
1110.707
2360.455
3410.412
4330.387
5120.385
6290.373
7190.372
8160.355
9300.280
10420.258

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Authority centrality

A node is authority-central to the extent that its in-links are from nodes that have many out-links. Individuals or organizations that act as authorities are receiving information from a wide range of others each of whom sends information to a large number of others. Technically, an agent is authority-central if its in-links are from agents that have are sending links to many others. The scientific name of this measure is authority centrality and it is calculated on agent by agent matrices.

Input network(s): network

RankSource nodesValue
1300.757
2260.517
3190.478
4100.440
5150.407
6420.344
7410.336
810.334
9360.238
10330.232

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Clique membership count

The number of distinct cliques to which each node belongs. Individuals or organizations who are high in number of cliques are those that belong to a large number of distinct cliques. A clique is defined as a group of three or more actors that have many connections to each other and relatively fewer connections to those in other groups. The scientific name of this measure is clique count and it is calculated on the agent by agent matrices.

Input network(s): network

RankSource nodesValue
1424.000
2303.000
312.000
4102.000
5112.000
6122.000
7152.000
8162.000
9172.000
10192.000

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Simmelian ties

The normalized number of Simmelian ties of each node.

Input network(s): network

RankSource nodesValueUnscaled
1400.0613.000
2450.0613.000
3460.0613.000
4470.0613.000
510.0412.000
6100.0412.000
7140.0412.000
8190.0412.000
9300.0412.000
10310.0412.000

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Clustering coefficient

Measures the degree of clustering in a network by averaging the clustering coefficient of each node, which is defined as the density of the node's ego network.

Input network(s): network

RankSource nodesValue
1221.000
2381.000
3431.000
4451.000
5471.000
6481.000
7140.833
810.583
950.500
10310.500

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Key Nodes Table

This shows the top scoring nodes side-by-side for selected measures.

RankBetweenness centralityCloseness centralityEigenvector centralityEigenvector centrality per componentIn-degree centralityIn-Closeness centralityOut-degree centralityTotal degree centrality
13737303030191117
23225111119301730
32121191926363746
41731363646411010
5303241414151219
61917262610292526
7292433331573611
833271117424636
936510102838137
102822424232261440

Produced by ORA developed at CASOS - Carnegie Mellon University