STANDARD NETWORK ANALYSIS REPORT

STANDARD NETWORK ANALYSIS REPORT

Input data: s50_d01 - 1

Start time: Fri Oct 14 13:34:14 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 count113.000
Density0.046
Components of 1 node (isolates)3
Components of 2 nodes (dyadic isolates)1
Components of 3 or more nodes4
Reciprocity0.527
Characteristic path length3.393
Clustering coefficient0.396
Network levels (diameter)8.000
Network fragmentation0.551
Krackhardt connectedness0.449
Krackhardt efficiency0.937
Krackhardt hierarchy0.617
Krackhardt upperboundedness0.827
Degree centralization0.069
Betweenness centralization0.082
Closeness centralization0.026
Eigenvector centralization0.424
Reciprocal (symmetric)?No (52% of the links are reciprocal)

Node Level Measures

MeasureMinMaxAvgStddev
Total degree centrality0.0000.1120.0460.024
Total degree centrality [Unscaled]0.00011.0004.5202.368
In-degree centrality0.0000.1630.0460.032
In-degree centrality [Unscaled]0.0008.0002.2601.560
Out-degree centrality0.0000.1020.0460.024
Out-degree centrality [Unscaled]0.0005.0002.2601.180
Eigenvector centrality0.0000.5380.1310.151
Eigenvector centrality [Unscaled]0.0000.3810.0920.107
Eigenvector centrality per component0.0000.2510.0720.063
Closeness centrality0.0200.0410.0280.007
Closeness centrality [Unscaled]0.0000.0010.0010.000
In-Closeness centrality0.0200.0520.0300.012
In-Closeness centrality [Unscaled]0.0000.0010.0010.000
Betweenness centrality0.0000.0940.0130.022
Betweenness centrality [Unscaled]0.000220.00030.58051.546
Hub centrality0.0000.4980.1350.147
Authority centrality0.0000.8040.1220.159
Information centrality-0.0010.0260.0200.011
Information centrality [Unscaled]-0.0000.0000.0000.000
Clique membership count0.0007.0001.6001.497
Simmelian ties0.0000.0410.0120.019
Simmelian ties [Unscaled]0.0002.0000.6000.917
Clustering coefficient0.0001.0000.3960.348

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: 0.0461225)

RankSource nodesValueUnscaledContext*
1110.11211.0002.229
2220.0929.0001.541
370.0828.0001.197
4240.0828.0001.197
5300.0828.0001.197
6310.0828.0001.197
7320.0828.0001.197
8170.0717.0000.853
9190.0717.0000.853
10460.0717.0000.853

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

Mean: 0.046Mean in random network: 0.046
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
1110.1638.000
270.1025.000
3210.1025.000
4220.1025.000
5310.1025.000
6300.0824.000
7320.0824.000
8440.0824.000
9460.0824.000
10100.0613.000

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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
1170.1025.000
2240.1025.000
3190.0824.000
4220.0824.000
5300.0824.000
6320.0824.000
770.0613.000
8100.0613.000
9110.0613.000
10120.0613.000

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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: 0.0461225)

RankSource nodesValueUnscaledContext*
1220.5380.3810.292
2210.4760.3370.065
3310.4630.3270.016
4170.4400.311-0.070
5240.4220.298-0.135
6190.3990.282-0.219
7320.3320.235-0.464
8250.2890.205-0.621
9300.2800.198-0.657
10110.2780.196-0.664

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

Mean: 0.131Mean in random network: 0.459
Std.dev: 0.151Std.dev in random network: 0.273

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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
1220.251
2210.222
3310.216
4170.205
5240.197
6190.186
7320.155
8250.135
9300.131
10110.130

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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: 0.0461225)

RankSource nodesValueUnscaledContext*
1430.0410.001-3.103
2390.0400.001-3.133
3170.0390.001-3.172
4190.0390.001-3.173
5240.0390.001-3.173
6220.0390.001-3.184
7180.0380.001-3.192
8230.0380.001-3.198
9250.0380.001-3.201
10210.0380.001-3.208

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

Mean: 0.028Mean in random network: 0.131
Std.dev: 0.007Std.dev in random network: 0.029

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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
1110.0520.001
220.0510.001
370.0510.001
4150.0510.001
5300.0510.001
6440.0510.001
7160.0500.001
8330.0500.001
9260.0500.001
10100.0500.001

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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: 0.0461225)

RankSource nodesValueUnscaledContext*
1220.094220.0000.181
2190.086202.0000.149
3170.075176.0000.103
4110.055128.8330.020
5300.03479.167-0.069
6260.03172.000-0.081
7210.03070.000-0.085
8310.02968.500-0.087
9240.02867.000-0.090
1070.02354.333-0.113

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

Mean: 0.013Mean in random network: 0.050
Std.dev: 0.022Std.dev in random network: 0.240

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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
1190.498
2300.488
3170.425
4240.397
5100.384
6150.327
7220.326
8140.317
9160.291
1020.287

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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
1110.804
2210.463
3220.367
4260.359
5310.336
6330.327
7300.312
8240.284
9190.255
10290.231

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Information centrality

Calculate the Stephenson and Zelen information centrality measure for each node.

Input network(s): network

RankSource nodesValueUnscaled
120.0260.000
270.0260.000
3110.0260.000
4190.0260.000
5300.0260.000
6260.0260.000
7150.0260.000
8100.0260.000
9120.0260.000
10170.0260.000

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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
1317.000
2115.000
3305.000
4194.000
5224.000
6173.000
7213.000
8263.000
9293.000
10323.000

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Simmelian ties

The normalized number of Simmelian ties of each node.

Input network(s): network

RankSource nodesValueUnscaled
130.0412.000
240.0412.000
370.0412.000
490.0412.000
5110.0412.000
6150.0412.000
7160.0412.000
8360.0412.000
9380.0412.000
10400.0412.000

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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
131.000
241.000
391.000
4121.000
5161.000
6361.000
7381.000
8411.000
9471.000
10481.000

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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
12243222211111711
219392121722422
317173131217197
41119171722152224
53024242431303030
62622191930443231
7211832323216732
83123252544331017
92425303046261119
10721111110101246

Produced by ORA developed at CASOS - Carnegie Mellon University