STANDARD NETWORK ANALYSIS REPORT

STANDARD NETWORK ANALYSIS REPORT

Input data: kf

Start time: Mon Oct 17 14:21:26 2011

Data Description

Calculates common social network measures on each selected input network.

Network agent x agent

Network Level Measures

MeasureValue
Row count21.000
Column count21.000
Link count102.000
Density0.243
Components of 1 node (isolates)0
Components of 2 nodes (dyadic isolates)0
Components of 3 or more nodes1
Reciprocity0.291
Characteristic path length2.103
Clustering coefficient0.413
Network levels (diameter)5.000
Network fragmentation0.000
Krackhardt connectedness1.000
Krackhardt efficiency0.689
Krackhardt hierarchy0.182
Krackhardt upperboundedness1.000
Degree centralization0.395
Betweenness centralization0.316
Closeness centralization0.947
Eigenvector centralization0.328
Reciprocal (symmetric)?No (29% of the links are reciprocal)

Node Level Measures

MeasureMinMaxAvgStddev
Total degree centrality0.0750.6000.2430.128
Total degree centrality [Unscaled]3.00024.0009.7145.119
In-degree centrality0.0500.5000.2430.108
In-degree centrality [Unscaled]1.00010.0004.8572.167
Out-degree centrality0.0000.9000.2430.218
Out-degree centrality [Unscaled]0.00018.0004.8574.367
Eigenvector centrality0.0940.5840.2870.114
Eigenvector centrality [Unscaled]0.0670.4130.2030.080
Eigenvector centrality per component0.0670.4130.2030.080
Closeness centrality0.0480.9090.4700.196
Closeness centrality [Unscaled]0.0020.0450.0230.010
In-Closeness centrality0.2080.3280.2590.027
In-Closeness centrality [Unscaled]0.0100.0160.0130.001
Betweenness centrality0.0000.3540.0530.079
Betweenness centrality [Unscaled]0.000134.43319.95230.068
Hub centrality0.0000.7930.2320.203
Authority centrality0.0880.5010.2880.111
Information centrality0.0000.0830.0480.023
Information centrality [Unscaled]0.0002.7591.5840.757
Clique membership count1.00026.0005.8105.404
Simmelian ties0.0000.2500.0670.084
Simmelian ties [Unscaled]0.0005.0001.3331.671
Clustering coefficient0.1791.0000.4130.162

Key Nodes

This chart shows the Agent that is repeatedly top-ranked in the measures listed below. The value shown is the percentage of measures for which the Agent 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: agent x agent (size: 21, density: 0.242857)

RankAgentValueUnscaledContext*
1170.60024.0003.817
2110.47519.0002.481
3190.35014.0001.145
410.32513.0000.878
520.32513.0000.878
650.32513.0000.878
7120.30012.0000.611
8150.30012.0000.611
940.27511.0000.344
10210.2259.000-0.191

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

Mean: 0.243Mean in random network: 0.243
Std.dev: 0.128Std.dev in random network: 0.094

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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): agent x agent

RankAgentValueUnscaled
120.50010.000
210.4008.000
3120.4008.000
450.3006.000
590.3006.000
6110.3006.000
7170.3006.000
830.2505.000
940.2505.000
1080.2505.000

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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): agent x agent

RankAgentValueUnscaled
1170.90018.000
2110.65013.000
3190.4509.000
4150.4008.000
550.3507.000
6100.3507.000
740.3006.000
860.3006.000
910.2505.000
10120.2004.000

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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: agent x agent (size: 21, density: 0.242857)

RankAgentValueUnscaledContext*
1170.5840.4130.196
2110.4750.336-0.178
3190.3970.281-0.446
420.3710.262-0.537
550.3670.260-0.549
610.3610.256-0.569
7150.3580.253-0.581
8120.3200.227-0.710
940.2850.202-0.830
10100.2730.193-0.873

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

Mean: 0.287Mean in random network: 0.527
Std.dev: 0.114Std.dev in random network: 0.291

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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): agent x agent

RankAgentValue
1170.413
2110.336
3190.281
420.262
550.260
610.256
7150.253
8120.227
940.202
10100.193

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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: agent x agent (size: 21, density: 0.242857)

RankAgentValueUnscaledContext*
1170.9090.0457.064
2110.7410.0374.144
3190.6250.0312.136
450.6060.0301.808
5150.6060.0301.808
640.5710.0291.207
760.5710.0291.207
8100.5410.0270.671
9120.5410.0270.671
10210.5410.0270.671

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

Mean: 0.470Mean in random network: 0.502
Std.dev: 0.196Std.dev in random network: 0.058

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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): agent x agent

RankAgentValueUnscaled
190.3280.016
270.3030.015
320.2900.014
410.2860.014
5120.2780.014
640.2630.013
780.2630.013
8170.2630.013
9180.2600.013
10210.2600.013

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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: agent x agent (size: 21, density: 0.242857)

RankAgentValueUnscaledContext*
1170.354134.4337.668
2110.15458.4502.409
3210.08933.9170.711
420.08833.4830.681
540.08331.6670.555
610.07629.0670.375
7150.05922.567-0.075
8190.05821.883-0.122
9120.05219.658-0.276
1050.04617.417-0.431

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

Mean: 0.053Mean in random network: 0.062
Std.dev: 0.079Std.dev in random network: 0.038

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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): agent x agent

RankAgentValue
1170.793
2110.611
3190.469
4150.383
5100.350
650.335
740.324
860.295
910.262
10210.200

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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): agent x agent

RankAgentValue
120.501
2120.473
310.431
490.396
550.388
630.373
780.335
8190.317
9110.307
10140.296

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Information centrality

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

Input network(s): agent x agent

RankAgentValueUnscaled
1170.0832.759
2110.0792.619
3190.0712.372
4150.0682.254
5100.0682.251
650.0672.242
760.0642.135
840.0602.000
910.0571.911
10210.0531.770

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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): agent x agent

RankAgentValue
11726.000
21114.000
3199.000
428.000
517.000
657.000
7157.000
8106.000
944.000
1064.000

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Simmelian ties

The normalized number of Simmelian ties of each node.

Input network(s): agent x agent

RankAgentValueUnscaled
1170.2505.000
2110.2004.000
3120.2004.000
440.1503.000
550.1503.000
6190.1503.000
710.1002.000
8150.1002.000
9210.1002.000

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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): agent x agent

RankAgentValue
1131.000
230.500
370.500
480.500
590.500
6160.500
740.476
8140.467
910.417
10210.400

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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
117171717291717
211111111171111
3211919191221919
4252251151
54155591252
61411114105
71561515178412
819101212317615
912124441814
1052110108211221

Produced by ORA developed at CASOS - Carnegie Mellon University