STANDARD NETWORK ANALYSIS REPORT

STANDARD NETWORK ANALYSIS REPORT

Input data: s50_d03 - 1

Start time: Fri Oct 14 13:35:30 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 count122.000
Density0.050
Components of 1 node (isolates)3
Components of 2 nodes (dyadic isolates)0
Components of 3 or more nodes4
Reciprocity0.584
Characteristic path length2.277
Clustering coefficient0.361
Network levels (diameter)8.000
Network fragmentation0.780
Krackhardt connectedness0.220
Krackhardt efficiency0.850
Krackhardt hierarchy0.462
Krackhardt upperboundedness0.890
Degree centralization0.076
Betweenness centralization0.017
Closeness centralization0.006
Eigenvector centralization0.576
Reciprocal (symmetric)?No (58% of the links are reciprocal)

Node Level Measures

MeasureMinMaxAvgStddev
Total degree centrality0.0000.1220.0500.028
Total degree centrality [Unscaled]0.00012.0004.8802.718
In-degree centrality0.0000.1430.0500.031
In-degree centrality [Unscaled]0.0007.0002.4401.512
Out-degree centrality0.0000.1020.0500.030
Out-degree centrality [Unscaled]0.0005.0002.4401.485
Eigenvector centrality0.0000.6480.0940.176
Eigenvector centrality [Unscaled]0.0000.4580.0670.125
Eigenvector centrality per component0.0000.1450.0540.043
Closeness centrality0.0200.0260.0230.002
Closeness centrality [Unscaled]0.0000.0010.0000.000
In-Closeness centrality0.0200.0260.0230.002
In-Closeness centrality [Unscaled]0.0000.0010.0000.000
Betweenness centrality0.0000.0200.0040.005
Betweenness centrality [Unscaled]0.00047.5838.84011.446
Hub centrality0.0000.6020.0920.177
Authority centrality0.0000.7530.0930.177
Information centrality-0.1192.1340.0200.313
Information centrality [Unscaled]-0.0000.0000.0000.000
Clique membership count0.0006.0001.2801.217
Simmelian ties0.0000.1020.0230.030
Simmelian ties [Unscaled]0.0005.0001.1201.451
Clustering coefficient0.0001.0000.3610.302

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: 0.0497959)

RankSource nodesValueUnscaledContext*
1330.12212.0002.362
2100.0929.0001.367
3110.0929.0001.367
4150.0929.0001.367
5360.0929.0001.367
6400.0929.0001.367
7460.0929.0001.367
870.0828.0001.035
9300.0828.0001.035
1010.0717.0000.703

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

Mean: 0.050Mean in random network: 0.050
Std.dev: 0.028Std.dev in random network: 0.031

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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
1330.1437.000
2150.1025.000
3400.1025.000
4460.1025.000
570.0824.000
6100.0824.000
7110.0824.000
8260.0824.000
9270.0824.000
10300.0824.000

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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
1100.1025.000
2110.1025.000
3330.1025.000
4360.1025.000
510.0824.000
670.0824.000
7140.0824.000
8150.0824.000
9210.0824.000
10290.0824.000

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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: 0.0497959)

RankSource nodesValueUnscaledContext*
1330.6480.4581.126
2110.5260.3720.668
3100.5050.3570.590
4150.4690.3320.452
5140.4420.3130.352
6290.3580.2530.034
710.3550.2510.020
8120.3530.2490.013
9300.3230.228-0.099
10360.2720.192-0.293

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

Mean: 0.094Mean in random network: 0.349
Std.dev: 0.176Std.dev in random network: 0.265

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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
1400.145
2460.129
3270.126
4330.119
5450.118
660.113
7240.113
8280.113
9470.107
10110.097

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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: 0.0497959)

RankSource nodesValueUnscaledContext*
1110.0260.001-4.958
2330.0260.001-4.958
3100.0260.001-4.958
4150.0260.001-4.958
5140.0260.001-4.959
6210.0260.001-4.959
7300.0260.001-4.959
8290.0260.001-4.959
910.0260.001-4.960
10360.0260.001-4.960

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

Mean: 0.023Mean in random network: 0.190
Std.dev: 0.002Std.dev in random network: 0.033

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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
1150.0260.001
2330.0260.001
3300.0260.001
4360.0260.001
5410.0260.001
6290.0260.001
7100.0260.001
8110.0260.001
9120.0260.001
10190.0260.001

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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: 0.0497959)

RankSource nodesValueUnscaledContext*
1330.02047.583-0.108
2360.01536.139-0.126
350.01432.000-0.133
4170.01330.000-0.136
5320.01330.000-0.136
6150.01126.889-0.141
740.01024.000-0.146
8270.01023.000-0.147
9300.00920.167-0.152
10400.00818.500-0.155

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

Mean: 0.004Mean in random network: 0.049
Std.dev: 0.005Std.dev in random network: 0.263

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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
1110.602
2100.519
3330.508
4140.496
5290.464
6300.379
7150.361
810.354
9360.351
10120.310

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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
1330.753
2150.537
3100.471
4110.451
510.389
6140.355
7300.352
8290.300
9190.287
10360.237

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Information centrality

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

Input network(s): network

RankSource nodesValueUnscaled
1442.1340.000
270.4580.000
3160.1780.000
4420.0710.000
5260.0710.000

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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
1336.000
273.000
3103.000
4113.000
5153.000
6293.000
7303.000
8403.000
9122.000
10142.000

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Simmelian ties

The normalized number of Simmelian ties of each node.

Input network(s): network

RankSource nodesValueUnscaled
1330.1025.000
2100.0824.000
3110.0824.000
4300.0824.000
5460.0824.000
610.0613.000
7140.0613.000
8290.0613.000
970.0412.000
10150.0412.000

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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
1311.000
260.833
3140.833
4280.833
5420.833
6480.833
7490.833
8160.750
9120.667
10190.667

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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
13311334033151033
23633114615331110
3510102740303311
41715153346363615
532141445741136
615212961029740
743012411101446
8272912282611157
9301304727122130
10403636113019291

Produced by ORA developed at CASOS - Carnegie Mellon University