STANDARD NETWORK ANALYSIS REPORT

STANDARD NETWORK ANALYSIS REPORT

Input data: szcig

Start time: Tue Oct 18 11:44:22 2011

Data Description

Calculates common social network measures on each selected input network.

Network

Network Level Measures

MeasureValue
Row count15.000
Column count15.000
Link count67.000
Density0.638
Components of 1 node (isolates)1
Components of 2 nodes (dyadic isolates)0
Components of 3 or more nodes1
Reciprocity1.000
Characteristic path length1.692
Clustering coefficient0.722
Network levels (diameter)3.000
Network fragmentation0.133
Krackhardt connectedness0.867
Krackhardt efficiency0.308
Krackhardt hierarchy0.000
Krackhardt upperboundedness1.000
Degree centralization0.117
Betweenness centralization0.118
Closeness centralization0.027
Eigenvector centralization0.229
Reciprocal (symmetric)?Yes

Node Level Measures

MeasureMinMaxAvgStddev
Total degree centrality0.0000.2860.1840.075
Total degree centrality [Unscaled]0.00024.00015.4676.334
In-degree centrality0.0000.2860.1840.075
In-degree centrality [Unscaled]0.00024.00015.4676.334
Out-degree centrality0.0000.2860.1840.075
Out-degree centrality [Unscaled]0.00024.00015.4676.334
Eigenvector centrality0.0000.5350.3370.141
Eigenvector centrality [Unscaled]0.0000.3790.2380.100
Eigenvector centrality per component0.0000.3530.2220.093
Closeness centrality0.0110.1300.1170.029
Closeness centrality [Unscaled]0.0010.0090.0080.002
In-Closeness centrality0.0110.1300.1170.029
In-Closeness centrality [Unscaled]0.0010.0090.0080.002
Betweenness centrality0.0000.1470.0370.046
Betweenness centrality [Unscaled]0.00013.4213.4104.173
Hub centrality0.0000.5350.3370.141
Authority centrality0.0000.5350.3370.141
Information centrality0.0000.0860.0670.021
Information centrality [Unscaled]0.00010.4798.1542.544
Clique membership count0.00012.0006.2673.530
Simmelian ties0.0000.8570.6380.209
Simmelian ties [Unscaled]0.00012.0008.9332.932
Clustering coefficient0.0000.8890.7220.199

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: 15, density: 0.638095)

RankAgentValueUnscaledContext*
1ALINZ0.28624.000-2.840
2DEUBK0.27423.000-2.936
3THYSN0.27423.000-2.936
4SIEMN0.26222.000-3.032
5RWE0.23820.000-3.224
6DIMLR0.20217.000-3.512
7VAG0.19016.000-3.608
8RUHRK0.19016.000-3.608
9KRUPP0.17915.000-3.704
10HAPAG0.15513.000-3.895

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

Mean: 0.184Mean in random network: 0.638
Std.dev: 0.075Std.dev in random network: 0.124

Back to top

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
1ALINZ0.28624.000
2DEUBK0.27423.000
3THYSN0.27423.000
4SIEMN0.26222.000
5RWE0.23820.000
6DIMLR0.20217.000
7VAG0.19016.000
8RUHRK0.19016.000
9KRUPP0.17915.000
10HAPAG0.15513.000

Back to top

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
1ALINZ0.28624.000
2DEUBK0.27423.000
3THYSN0.27423.000
4SIEMN0.26222.000
5RWE0.23820.000
6DIMLR0.20217.000
7VAG0.19016.000
8RUHRK0.19016.000
9KRUPP0.17915.000
10HAPAG0.15513.000

Back to top

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: 15, density: 0.638095)

RankAgentValueUnscaledContext*
1ALINZ0.5350.379-0.975
2SIEMN0.5220.369-1.035
3THYSN0.4970.351-1.147
4DEUBK0.4860.344-1.194
5RWE0.4130.292-1.523
6DIMLR0.4070.288-1.548
7RUHRK0.3420.242-1.838
8VAG0.3220.228-1.926
9KRUPP0.3060.217-1.997
10HAPAG0.2870.203-2.086

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

Mean: 0.337Mean in random network: 0.754
Std.dev: 0.141Std.dev in random network: 0.224

Back to top

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
1ALINZ0.353
2SIEMN0.344
3THYSN0.328
4DEUBK0.321
5RWE0.272
6DIMLR0.269
7RUHRK0.226
8VAG0.213
9KRUPP0.202
10HAPAG0.189

Back to top

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: 15, density: 0.638095)

RankAgentValueUnscaledContext*
1RUHRK0.1300.009-11.459
2DRESB0.1300.009-11.459
3HAPAG0.1280.009-11.482
4KARST0.1270.009-11.504
5ALINZ0.1260.009-11.526
6VAG0.1250.009-11.548
7RWE0.1250.009-11.548
8KREDT0.1250.009-11.548
9DIMLR0.1240.009-11.570
10KRUPP0.1240.009-11.570

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

Mean: 0.117Mean in random network: 0.721
Std.dev: 0.029Std.dev in random network: 0.052

Back to top

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
1RUHRK0.1300.009
2DRESB0.1300.009
3HAPAG0.1280.009
4KARST0.1270.009
5ALINZ0.1260.009
6VAG0.1250.009
7RWE0.1250.009
8KREDT0.1250.009
9DIMLR0.1240.009
10KRUPP0.1240.009

Back to top

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: 15, density: 0.638095)

RankAgentValueUnscaledContext*
1RUHRK0.14713.4212.384
2DRESB0.12211.1361.899
3HAPAG0.0999.0371.455
4KARST0.0474.3100.452
5KREDT0.0474.2420.438
6ALINZ0.0222.033-0.030
7VAG0.0201.783-0.083
8DEUBK0.0181.625-0.117
9THYSN0.0141.262-0.194
10KRUPP0.0121.083-0.232

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

Mean: 0.037Mean in random network: 0.024
Std.dev: 0.046Std.dev in random network: 0.052

Back to top

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
1ALINZ0.535
2SIEMN0.522
3THYSN0.497
4DEUBK0.486
5RWE0.413
6DIMLR0.407
7RUHRK0.342
8VAG0.322
9KRUPP0.306
10HAPAG0.287

Back to top

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
1ALINZ0.535
2SIEMN0.522
3THYSN0.497
4DEUBK0.486
5RWE0.413
6DIMLR0.407
7RUHRK0.342
8VAG0.322
9KRUPP0.306
10HAPAG0.287

Back to top

Information centrality

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

Input network(s): agent x agent

RankAgentValueUnscaled
1ALINZ0.08610.479
2DEUBK0.08510.384
3THYSN0.08510.372
4SIEMN0.0819.880
5RWE0.0809.817
6DIMLR0.0749.028
7RUHRK0.0738.922
8VAG0.0738.874
9KRUPP0.0708.516
10HAPAG0.0657.969

Back to top

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
1ALINZ12.000
2RUHRK11.000
3RWE11.000
4DEUBK10.000
5VAG9.000
6THYSN8.000
7HAPAG6.000
8DRESB5.000
9KARST5.000
10DIMLR4.000

Back to top

Simmelian ties

The normalized number of Simmelian ties of each node.

Input network(s): agent x agent

RankAgentValueUnscaled
1ALINZ0.85712.000
2RUHRK0.85712.000
3DEUBK0.78611.000
4RWE0.78611.000
5THYSN0.78611.000
6VAG0.71410.000
7HAPAG0.71410.000
8DRESB0.71410.000
9DIMLR0.6439.000
10KRUPP0.6439.000

Back to top

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
1DIMLR0.889
2KRUPP0.833
3SIEMN0.821
4HAPAG0.800
5MANES0.800
6RWE0.782
7THYSN0.782
8DRESB0.778
9KARST0.762
10VAG0.733

Back to top

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
1RUHRKRUHRKALINZALINZALINZRUHRKALINZALINZ
2DRESBDRESBSIEMNSIEMNDEUBKDRESBDEUBKDEUBK
3HAPAGHAPAGTHYSNTHYSNTHYSNHAPAGTHYSNTHYSN
4KARSTKARSTDEUBKDEUBKSIEMNKARSTSIEMNSIEMN
5KREDTALINZRWERWERWEALINZRWERWE
6ALINZVAGDIMLRDIMLRDIMLRVAGDIMLRDIMLR
7VAGRWERUHRKRUHRKVAGRWEVAGVAG
8DEUBKKREDTVAGVAGRUHRKKREDTRUHRKRUHRK
9THYSNDIMLRKRUPPKRUPPKRUPPDIMLRKRUPPKRUPP
10KRUPPKRUPPHAPAGHAPAGHAPAGKRUPPHAPAGHAPAG

Produced by ORA developed at CASOS - Carnegie Mellon University