Calculates common social network measures on each selected input network.
Network agent x agent
Network Level Measures
Measure Value Row count 73.000 Column count 73.000 Link count 61.000 Density 0.023 Components of 1 node (isolates) 37 Components of 2 nodes (dyadic isolates) 0 Components of 3 or more nodes 2 Reciprocity 1.000 Characteristic path length 3.182 Clustering coefficient 0.230 Network levels (diameter) 7.000 Network fragmentation 0.829 Krackhardt connectedness 0.171 Krackhardt efficiency 0.935 Krackhardt hierarchy 0.000 Krackhardt upperboundedness 1.000 Degree centralization 0.090 Betweenness centralization 0.042 Closeness centralization 0.011 Eigenvector centralization 0.546 Reciprocal (symmetric)? Yes
Node Level Measures
Measure Min Max Avg Stddev Total degree centrality 0.000 0.111 0.023 0.031 Total degree centrality [Unscaled] 0.000 40.000 8.356 11.228 In-degree centrality 0.000 0.111 0.023 0.031 In-degree centrality [Unscaled] 0.000 40.000 8.356 11.228 Out-degree centrality 0.000 0.111 0.023 0.031 Out-degree centrality [Unscaled] 0.000 40.000 8.356 11.228 Eigenvector centrality 0.000 0.597 0.066 0.152 Eigenvector centrality [Unscaled] 0.000 0.422 0.047 0.107 Eigenvector centrality per component 0.000 0.173 0.022 0.044 Closeness centrality 0.014 0.023 0.018 0.004 Closeness centrality [Unscaled] 0.000 0.000 0.000 0.000 In-Closeness centrality 0.014 0.023 0.018 0.004 In-Closeness centrality [Unscaled] 0.000 0.000 0.000 0.000 Betweenness centrality 0.000 0.047 0.005 0.012 Betweenness centrality [Unscaled] 0.000 120.410 13.452 30.214 Hub centrality 0.000 0.597 0.066 0.152 Authority centrality 0.000 0.597 0.066 0.152 Information centrality 0.000 0.033 0.014 0.016 Information centrality [Unscaled] 0.000 0.000 0.000 0.000 Clique membership count 0.000 3.000 0.534 0.861 Simmelian ties 0.000 0.097 0.018 0.028 Simmelian ties [Unscaled] 0.000 7.000 1.288 2.051 Clustering coefficient 0.000 1.000 0.230 0.369
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: 73, density: 0.0232116)
Rank Agent Value Unscaled Context* 1 Nawaf Alhazmi 0.111 40.000 4.988 2 Mohamed Atta 0.111 40.000 4.988 3 Marwan Al-Shehhi 0.111 40.000 4.988 4 Ziad Jarrah 0.097 35.000 4.200 5 Hani Hanjour 0.083 30.000 3.411 6 Hamza Alghamdi 0.083 30.000 3.411 7 Lotfi Raissi 0.069 25.000 2.623 8 Said Bahaji 0.069 25.000 2.623 9 Ramzi Bin al-Shibh 0.069 25.000 2.623 10 Zakariya Essabar 0.069 25.000 2.623 * Number of standard deviations from the mean of a random network of the same size and density
Mean: 0.023 Mean in random network: 0.023 Std.dev: 0.031 Std.dev in random network: 0.018 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 Nawaf Alhazmi 0.111 40.000 2 Mohamed Atta 0.111 40.000 3 Marwan Al-Shehhi 0.111 40.000 4 Ziad Jarrah 0.097 35.000 5 Hani Hanjour 0.083 30.000 6 Hamza Alghamdi 0.083 30.000 7 Lotfi Raissi 0.069 25.000 8 Said Bahaji 0.069 25.000 9 Ramzi Bin al-Shibh 0.069 25.000 10 Zakariya Essabar 0.069 25.000 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 Nawaf Alhazmi 0.111 40.000 2 Mohamed Atta 0.111 40.000 3 Marwan Al-Shehhi 0.111 40.000 4 Ziad Jarrah 0.097 35.000 5 Hani Hanjour 0.083 30.000 6 Hamza Alghamdi 0.083 30.000 7 Lotfi Raissi 0.069 25.000 8 Said Bahaji 0.069 25.000 9 Ramzi Bin al-Shibh 0.069 25.000 10 Zakariya Essabar 0.069 25.000 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: 73, density: 0.0232116)
Rank Agent Value Unscaled Context* 1 Marwan Al-Shehhi 0.597 0.422 -2.316 2 Mohamed Atta 0.596 0.421 -2.319 3 Ziad Jarrah 0.563 0.398 -2.443 4 Said Bahaji 0.492 0.348 -2.714 5 Ramzi Bin al-Shibh 0.492 0.348 -2.714 6 Zakariya Essabar 0.492 0.348 -2.714 7 Lotfi Raissi 0.350 0.247 -3.253 8 Abdul Aziz Al-Omari* 0.222 0.157 -3.739 9 Ahmed Al Haznawi 0.119 0.084 -4.131 10 Fayez Ahmed 0.116 0.082 -4.140 * Number of standard deviations from the mean of a random network of the same size and density
Mean: 0.066 Mean in random network: 1.206 Std.dev: 0.152 Std.dev in random network: 0.263 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 Marwan Al-Shehhi 0.173 2 Mohamed Atta 0.173 3 Ziad Jarrah 0.164 4 Said Bahaji 0.143 5 Ramzi Bin al-Shibh 0.143 6 Zakariya Essabar 0.143 7 Lotfi Raissi 0.102 8 Abdul Aziz Al-Omari* 0.064 9 Zacarias Moussaoui 0.052 10 Jerome Courtaillier 0.037 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: 73, density: 0.0232116)
Rank Agent Value Unscaled Context* 1 Marwan Al-Shehhi 0.023 0.000 47.905 2 Lotfi Raissi 0.023 0.000 47.905 3 Mohamed Atta 0.023 0.000 47.904 4 Ziad Jarrah 0.023 0.000 47.904 5 Hani Hanjour 0.023 0.000 47.903 6 Nawaf Alhazmi 0.023 0.000 47.900 7 Hamza Alghamdi 0.023 0.000 47.900 8 Ahmed Al Haznawi 0.023 0.000 47.900 9 Fayez Ahmed 0.023 0.000 47.899 10 Saeed Alghamdi* 0.023 0.000 47.898 * Number of standard deviations from the mean of a random network of the same size and density
Mean: 0.018 Mean in random network: -0.121 Std.dev: 0.004 Std.dev in random network: 0.003 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 Marwan Al-Shehhi 0.023 0.000 2 Lotfi Raissi 0.023 0.000 3 Mohamed Atta 0.023 0.000 4 Ziad Jarrah 0.023 0.000 5 Hani Hanjour 0.023 0.000 6 Nawaf Alhazmi 0.023 0.000 7 Hamza Alghamdi 0.023 0.000 8 Ahmed Al Haznawi 0.023 0.000 9 Fayez Ahmed 0.023 0.000 10 Saeed Alghamdi* 0.023 0.000 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: 73, density: 0.0232116)
Rank Agent Value Unscaled Context* 1 Hani Hanjour 0.047 120.410 0.095 2 Lotfi Raissi 0.045 115.826 0.070 3 Mohamed Atta 0.039 99.081 -0.020 4 Nawaf Alhazmi 0.037 95.476 -0.040 5 Marwan Al-Shehhi 0.037 94.319 -0.046 6 Abdul Aziz Al-Omari* 0.031 78.000 -0.134 7 Ziad Jarrah 0.026 66.386 -0.197 8 Hamza Alghamdi 0.026 66.248 -0.198 9 Waleed Alshehri 0.021 54.000 -0.264 10 Ahmed Al Haznawi 0.019 49.352 -0.289 * Number of standard deviations from the mean of a random network of the same size and density
Mean: 0.005 Mean in random network: 0.040 Std.dev: 0.012 Std.dev in random network: 0.072 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 Marwan Al-Shehhi 0.597 2 Mohamed Atta 0.596 3 Ziad Jarrah 0.563 4 Said Bahaji 0.492 5 Ramzi Bin al-Shibh 0.492 6 Zakariya Essabar 0.492 7 Lotfi Raissi 0.350 8 Abdul Aziz Al-Omari* 0.222 9 Ahmed Al Haznawi 0.119 10 Fayez Ahmed 0.116 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 Marwan Al-Shehhi 0.597 2 Mohamed Atta 0.596 3 Ziad Jarrah 0.563 4 Said Bahaji 0.492 5 Ramzi Bin al-Shibh 0.492 6 Zakariya Essabar 0.492 7 Lotfi Raissi 0.350 8 Abdul Aziz Al-Omari* 0.222 9 Ahmed Al Haznawi 0.119 10 Fayez Ahmed 0.116 Information centrality
Calculate the Stephenson and Zelen information centrality measure for each node.
Input network(s): agent x agent
Rank Agent Value Unscaled 1 Marwan Al-Shehhi 0.033 0.000 2 Ziad Jarrah 0.033 0.000 3 Mohamed Atta 0.033 0.000 4 Nawaf Alhazmi 0.033 0.000 5 Hamza Alghamdi 0.033 0.000 6 Lotfi Raissi 0.033 0.000 7 Ahmed Al Haznawi 0.033 0.000 8 Hani Hanjour 0.033 0.000 9 Saeed Alghamdi* 0.033 0.000 10 Said Bahaji 0.033 0.000 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 Hani Hanjour 3.000 2 Nawaf Alhazmi 3.000 3 Mohamed Atta 3.000 4 Marwan Al-Shehhi 3.000 5 Khalid Al-Mihdhar 2.000 6 Hamza Alghamdi 2.000 7 Ziad Jarrah 2.000 8 Saeed Alghamdi* 2.000 9 Lotfi Raissi 2.000 10 Rayed Mohammed Abdullah 2.000 Simmelian ties
The normalized number of Simmelian ties of each node.
Input network(s): agent x agent
Rank Agent Value Unscaled 1 Nawaf Alhazmi 0.097 7.000 2 Mohamed Atta 0.097 7.000 3 Marwan Al-Shehhi 0.097 7.000 4 Ziad Jarrah 0.083 6.000 5 Hani Hanjour 0.069 5.000 6 Lotfi Raissi 0.069 5.000 7 Said Bahaji 0.069 5.000 8 Ramzi Bin al-Shibh 0.069 5.000 9 Zakariya Essabar 0.069 5.000 10 Khalid Al-Mihdhar 0.056 4.000 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 Wail Alshehri 1.000 2 Satam Suqami 1.000 3 Ahmed Alnami 1.000 4 Abdussattar Shaikh 1.000 5 Said Bahaji 1.000 6 Ramzi Bin al-Shibh 1.000 7 Bandar Alhazmi 1.000 8 Zakariya Essabar 1.000 9 Osama Awadallah 1.000 10 Jerome Courtaillier 1.000
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 Hani Hanjour Marwan Al-Shehhi Marwan Al-Shehhi Marwan Al-Shehhi Nawaf Alhazmi Marwan Al-Shehhi Nawaf Alhazmi Nawaf Alhazmi 2 Lotfi Raissi Lotfi Raissi Mohamed Atta Mohamed Atta Mohamed Atta Lotfi Raissi Mohamed Atta Mohamed Atta 3 Mohamed Atta Mohamed Atta Ziad Jarrah Ziad Jarrah Marwan Al-Shehhi Mohamed Atta Marwan Al-Shehhi Marwan Al-Shehhi 4 Nawaf Alhazmi Ziad Jarrah Said Bahaji Said Bahaji Ziad Jarrah Ziad Jarrah Ziad Jarrah Ziad Jarrah 5 Marwan Al-Shehhi Hani Hanjour Ramzi Bin al-Shibh Ramzi Bin al-Shibh Hani Hanjour Hani Hanjour Hani Hanjour Hani Hanjour 6 Abdul Aziz Al-Omari* Nawaf Alhazmi Zakariya Essabar Zakariya Essabar Hamza Alghamdi Nawaf Alhazmi Hamza Alghamdi Hamza Alghamdi 7 Ziad Jarrah Hamza Alghamdi Lotfi Raissi Lotfi Raissi Lotfi Raissi Hamza Alghamdi Lotfi Raissi Lotfi Raissi 8 Hamza Alghamdi Ahmed Al Haznawi Abdul Aziz Al-Omari* Abdul Aziz Al-Omari* Said Bahaji Ahmed Al Haznawi Said Bahaji Said Bahaji 9 Waleed Alshehri Fayez Ahmed Ahmed Al Haznawi Zacarias Moussaoui Ramzi Bin al-Shibh Fayez Ahmed Ramzi Bin al-Shibh Ramzi Bin al-Shibh 10 Ahmed Al Haznawi Saeed Alghamdi* Fayez Ahmed Jerome Courtaillier Zakariya Essabar Saeed Alghamdi* Zakariya Essabar Zakariya Essabar