Network Level Measures
Measure Value Row count 16.000 Column count 16.000 Link count 28.000 Density 0.117 Components of 1 node (isolates) 4 Components of 2 nodes (dyadic isolates) 0 Components of 3 or more nodes 1 Reciprocity 0.867 Characteristic path length 2.281 Clustering coefficient 0.237 Network levels (diameter) 4.000 Network fragmentation 0.450 Krackhardt connectedness 0.550 Krackhardt efficiency 0.927 Krackhardt hierarchy 0.167 Krackhardt upperboundedness 1.000 Degree centralization 0.324 Betweenness centralization 0.200 Closeness centralization 0.066 Eigenvector centralization 0.526 Reciprocal (symmetric)? No (86% of the links are reciprocal)
Node Level Measures
Measure Min Max Avg Stddev Total degree centrality 0.000 0.400 0.117 0.112 Total degree centrality [Unscaled] 0.000 12.000 3.500 3.373 In-degree centrality 0.000 0.400 0.117 0.114 In-degree centrality [Unscaled] 0.000 6.000 1.750 1.714 Out-degree centrality 0.000 0.400 0.117 0.112 Out-degree centrality [Unscaled] 0.000 6.000 1.750 1.677 Eigenvector centrality 0.000 0.735 0.274 0.223 Eigenvector centrality [Unscaled] 0.000 0.520 0.194 0.158 Eigenvector centrality per component 0.000 0.390 0.146 0.118 Closeness centrality 0.063 0.156 0.126 0.037 Closeness centrality [Unscaled] 0.004 0.010 0.008 0.002 In-Closeness centrality 0.063 0.181 0.136 0.050 In-Closeness centrality [Unscaled] 0.004 0.012 0.009 0.003 Betweenness centrality 0.000 0.233 0.046 0.080 Betweenness centrality [Unscaled] 0.000 49.000 9.688 16.886 Hub centrality 0.000 0.798 0.264 0.235 Authority centrality 0.000 0.729 0.265 0.234 Information centrality 0.000 0.120 0.062 0.041 Information centrality [Unscaled] 0.000 1.272 0.661 0.431 Clique membership count 0.000 2.000 0.563 0.704 Simmelian ties 0.000 0.200 0.067 0.078 Simmelian ties [Unscaled] 0.000 3.000 1.000 1.173 Clustering coefficient 0.000 1.000 0.238 0.378
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: 16, density: 0.116667)
Rank Agent Value Unscaled Context* 1 Wadih al Hage 0.400 12.000 3.530 2 Mohammed Rashed Daoud al-Owhali 0.267 8.000 1.869 3 Usama Bin Ladin 0.267 8.000 1.869 4 Abdullah Ahmed Abdullah 0.200 6.000 1.038 5 Ali Mohammed 0.133 4.000 0.208 6 al-Fawwaz 0.133 4.000 0.208 7 Abdal Rahmad 0.133 4.000 0.208 8 Mohammed Sadiq Odeh 0.100 3.000 -0.208 9 Fazul Abdullah Mohammed 0.067 2.000 -0.623 10 Jihad Mohammed Ali 0.067 2.000 -0.623 * Number of standard deviations from the mean of a random network of the same size and density
Mean: 0.117 Mean in random network: 0.117 Std.dev: 0.112 Std.dev in random network: 0.080 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
Rank Agent Value Unscaled 1 Wadih al Hage 0.400 6.000 2 Mohammed Rashed Daoud al-Owhali 0.267 4.000 3 Usama Bin Ladin 0.267 4.000 4 Abdullah Ahmed Abdullah 0.200 3.000 5 Mohammed Sadiq Odeh 0.133 2.000 6 Ali Mohammed 0.133 2.000 7 al-Fawwaz 0.133 2.000 8 Abdal Rahmad 0.133 2.000 9 Fazul Abdullah Mohammed 0.067 1.000 10 Jihad Mohammed Ali 0.067 1.000 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
Rank Agent Value Unscaled 1 Wadih al Hage 0.400 6.000 2 Mohammed Rashed Daoud al-Owhali 0.267 4.000 3 Usama Bin Ladin 0.267 4.000 4 Abdullah Ahmed Abdullah 0.200 3.000 5 Ali Mohammed 0.133 2.000 6 al-Fawwaz 0.133 2.000 7 Abdal Rahmad 0.133 2.000 8 Mohammed Sadiq Odeh 0.067 1.000 9 Ahmed the German 0.067 1.000 10 Fazul Abdullah Mohammed 0.067 1.000 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: 16, density: 0.116667)
Rank Agent Value Unscaled Context* 1 Wadih al Hage 0.735 0.520 1.104 2 Usama Bin Ladin 0.647 0.458 0.849 3 Mohammed Rashed Daoud al-Owhali 0.445 0.315 0.264 4 Ali Mohammed 0.436 0.308 0.237 5 al-Fawwaz 0.436 0.308 0.237 6 Abdullah Ahmed Abdullah 0.367 0.260 0.038 7 Mohammed Sadiq Odeh 0.348 0.246 -0.019 8 Abdal Rahmad 0.256 0.181 -0.284 9 Fazul Abdullah Mohammed 0.232 0.164 -0.355 10 abouhalima 0.232 0.164 -0.355 * Number of standard deviations from the mean of a random network of the same size and density
Mean: 0.274 Mean in random network: 0.354 Std.dev: 0.223 Std.dev in random network: 0.345 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
Rank Agent Value 1 Wadih al Hage 0.390 2 Usama Bin Ladin 0.343 3 Mohammed Rashed Daoud al-Owhali 0.236 4 Ali Mohammed 0.231 5 al-Fawwaz 0.231 6 Abdullah Ahmed Abdullah 0.195 7 Mohammed Sadiq Odeh 0.184 8 Abdal Rahmad 0.136 9 Fazul Abdullah Mohammed 0.123 10 abouhalima 0.123 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: 16, density: 0.116667)
Rank Agent Value Unscaled Context* 1 Ahmed the German 0.156 0.010 -2.846 2 Usama Bin Ladin 0.156 0.010 -2.846 3 Wadih al Hage 0.155 0.010 -2.881 4 Mohammed Rashed Daoud al-Owhali 0.153 0.010 -2.915 5 Ali Mohammed 0.149 0.010 -3.014 6 al-Fawwaz 0.149 0.010 -3.014 7 Abdullah Ahmed Abdullah 0.149 0.010 -3.014 8 Abdal Rahmad 0.143 0.010 -3.136 9 Mohammed Sadiq Odeh 0.142 0.009 -3.166 10 Fazul Abdullah Mohammed 0.142 0.009 -3.166 * Number of standard deviations from the mean of a random network of the same size and density
Mean: 0.126 Mean in random network: 0.288 Std.dev: 0.037 Std.dev in random network: 0.046 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
Rank Agent Value Unscaled 1 Wadih al Hage 0.181 0.012 2 Usama Bin Ladin 0.181 0.012 3 Mohammed Rashed Daoud al-Owhali 0.176 0.012 4 Mohammed Sadiq Odeh 0.176 0.012 5 Ali Mohammed 0.169 0.011 6 al-Fawwaz 0.169 0.011 7 Abdullah Ahmed Abdullah 0.163 0.011 8 Fazul Abdullah Mohammed 0.161 0.011 9 abouhalima 0.161 0.011 10 Abdal Rahmad 0.161 0.011 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: 16, density: 0.116667)
Rank Agent Value Unscaled Context* 1 Wadih al Hage 0.233 49.000 1.410 2 Mohammed Rashed Daoud al-Owhali 0.198 41.500 0.980 3 Usama Bin Ladin 0.193 40.500 0.922 4 Abdullah Ahmed Abdullah 0.069 14.500 -0.569 5 Mohammed Sadiq Odeh 0.045 9.500 -0.856 * Number of standard deviations from the mean of a random network of the same size and density
Mean: 0.046 Mean in random network: 0.116 Std.dev: 0.080 Std.dev in random network: 0.083 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
Rank Agent Value 1 Wadih al Hage 0.798 2 Usama Bin Ladin 0.676 3 Ali Mohammed 0.449 4 al-Fawwaz 0.449 5 Mohammed Rashed Daoud al-Owhali 0.402 6 Abdullah Ahmed Abdullah 0.330 7 Mohammed Sadiq Odeh 0.234 8 Fazul Abdullah Mohammed 0.234 9 abouhalima 0.234 10 Abdal Rahmad 0.209 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
Rank Agent Value 1 Wadih al Hage 0.729 2 Usama Bin Ladin 0.673 3 Ali Mohammed 0.472 4 al-Fawwaz 0.472 5 Mohammed Rashed Daoud al-Owhali 0.434 6 Mohammed Sadiq Odeh 0.362 7 Fazul Abdullah Mohammed 0.256 8 abouhalima 0.256 9 Abdal Rahmad 0.235 10 Abdullah Ahmed Abdullah 0.218 Information centrality
Calculate the Stephenson and Zelen information centrality measure for each node.
Input network(s): Agent x Agent
Rank Agent Value Unscaled 1 Wadih al Hage 0.120 1.272 2 Usama Bin Ladin 0.115 1.212 3 Abdullah Ahmed Abdullah 0.105 1.108 4 Mohammed Rashed Daoud al-Owhali 0.103 1.087 5 Ali Mohammed 0.086 0.911 6 al-Fawwaz 0.086 0.911 7 Abdal Rahmad 0.078 0.822 8 Mohammed Sadiq Odeh 0.069 0.729 9 Ahmed the German 0.066 0.698 10 abouhalima 0.060 0.629 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
Rank Agent Value 1 Wadih al Hage 2.000 2 Usama Bin Ladin 2.000 3 Mohammed Rashed Daoud al-Owhali 1.000 4 Ali Mohammed 1.000 5 al-Fawwaz 1.000 6 Abdullah Ahmed Abdullah 1.000 7 Abdal Rahmad 1.000 Simmelian ties
The normalized number of Simmelian ties of each node.
Input network(s): Agent x Agent
Rank Agent Value Unscaled 1 Wadih al Hage 0.200 3.000 2 Usama Bin Ladin 0.200 3.000 3 Mohammed Rashed Daoud al-Owhali 0.133 2.000 4 Ali Mohammed 0.133 2.000 5 al-Fawwaz 0.133 2.000 6 Abdullah Ahmed Abdullah 0.133 2.000 7 Abdal Rahmad 0.133 2.000 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
Rank Agent Value 1 Ali Mohammed 1.000 2 al-Fawwaz 1.000 3 Abdal Rahmad 1.000 4 Usama Bin Ladin 0.333 5 Mohammed Rashed Daoud al-Owhali 0.167 6 Abdullah Ahmed Abdullah 0.167 7 Wadih al Hage 0.133
Key Nodes Table
This shows the top scoring nodes side-by-side for selected measures.
Rank Betweenness centrality Closeness centrality Eigenvector centrality Eigenvector centrality per component In-degree centrality In-Closeness centrality Out-degree centrality Total degree centrality 1 Wadih al Hage Ahmed the German Wadih al Hage Wadih al Hage Wadih al Hage Wadih al Hage Wadih al Hage Wadih al Hage 2 Mohammed Rashed Daoud al-Owhali Usama Bin Ladin Usama Bin Ladin Usama Bin Ladin Mohammed Rashed Daoud al-Owhali Usama Bin Ladin Mohammed Rashed Daoud al-Owhali Mohammed Rashed Daoud al-Owhali 3 Usama Bin Ladin Wadih al Hage Mohammed Rashed Daoud al-Owhali Mohammed Rashed Daoud al-Owhali Usama Bin Ladin Mohammed Rashed Daoud al-Owhali Usama Bin Ladin Usama Bin Ladin 4 Abdullah Ahmed Abdullah Mohammed Rashed Daoud al-Owhali Ali Mohammed Ali Mohammed Abdullah Ahmed Abdullah Mohammed Sadiq Odeh Abdullah Ahmed Abdullah Abdullah Ahmed Abdullah 5 Mohammed Sadiq Odeh Ali Mohammed al-Fawwaz al-Fawwaz Mohammed Sadiq Odeh Ali Mohammed Ali Mohammed Ali Mohammed 6 Khalfan Khamis Mohamed al-Fawwaz Abdullah Ahmed Abdullah Abdullah Ahmed Abdullah Ali Mohammed al-Fawwaz al-Fawwaz al-Fawwaz 7 Ahmed the German Abdullah Ahmed Abdullah Mohammed Sadiq Odeh Mohammed Sadiq Odeh al-Fawwaz Abdullah Ahmed Abdullah Abdal Rahmad Abdal Rahmad 8 Fazul Abdullah Mohammed Abdal Rahmad Abdal Rahmad Abdal Rahmad Abdal Rahmad Fazul Abdullah Mohammed Mohammed Sadiq Odeh Mohammed Sadiq Odeh 9 Ali Mohammed Mohammed Sadiq Odeh Fazul Abdullah Mohammed Fazul Abdullah Mohammed Fazul Abdullah Mohammed abouhalima Ahmed the German Fazul Abdullah Mohammed 10 Ahmed Khalfan Ghailani Fazul Abdullah Mohammed abouhalima abouhalima Jihad Mohammed Ali Abdal Rahmad Fazul Abdullah Mohammed Jihad Mohammed Ali