Table 1

The network topological indexes used in this study
Indexes Formula Explanation Note Ref
Part I: network indexes for individual nodes
Connectivity <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M1">View MathML</a> <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M2">View MathML</a>is the connection strength between nodes i and j. It is also called node degree. It is the most commonly used concept for desibing the topological property of a node in a network. [33]
Stress centrality <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M3">View MathML</a> <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M4">View MathML</a> is the number of shortest paths between nodes j and k that pass through node i. It is used to desibe the number of geodesic paths that pass through the ith node. High Stress node can serve as a broker. [34]
Betweenness <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M5">View MathML</a> <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M6">View MathML</a> is the total number of shortest paths between j and k. It is used to desibe the ratio of paths that pass through the ith node. High Betweenness node can serve as a broker similar to stress centrality. [34]
Eigenvector centrality <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M7','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M7">View MathML</a> M(i) is the set of nodes that are connected to the ith node and λ is a constant eigenvalue. It is used to desibe the degree of a central node that it is connected to other central nodes. [35]
Clustering coefficient <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M8">View MathML</a> li is the number of links between neighbors of node i and ki is the number of neighbors of node i. It desibes how well a node is connected with its neighbors. If it is fully connected to its neighbors, the clustering coefficient is 1. A value close to 0 means that there are hardly any connections with its neighbors. It was used to desibe hierarchical properties of networks. [36,37]
Vulnerability <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M9','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M9">View MathML</a> E is the global efficiency and Ei is the global efficiency after the removal of the node i and its entire links. It measures the deease of node i on the system performance if node i and all associated links are removed. [38]
Part II: The overall network topological indexes
Average connectivity <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M10','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M10">View MathML</a> ki is degree of node i and n is the number of nodes. Higher avgK means a more complex network. [39]
Average geodesic distance <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M11','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M11">View MathML</a> dij is the shortest path between node i and j. A smaller GD means all the nodes in the network are closer. [39]
Geodesic efficiency <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M12','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M12">View MathML</a> all parameters shown above. It is the opposite of GD. A higher E means that the nodes are closer. [40]
Harmonic geodesic distance <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M13','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M13">View MathML</a> E is geodesic efficiency. The reciprocal of E, which is similar to GD but more appropriate for disjoint graph. [40]
Centralization of degree <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M14','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M14">View MathML</a> max(k) is the maximal value of all connectivity values and ki represents the connectivity of ith node. Finally this value is normalized by the theoretical maximum centralization score. It is close to 1 for a network with star topology and in contrast close to 0 for a network where each node has the same connectivity. [41]
Centralization of betweenness <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M15','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M15">View MathML</a> max(B) is the maximal value of all betweenness values and Bi represents the betweenness of ith node. Finally this value is normalized by the theoretical maximum centralization score. It is close to 0 for a network where each node has the same betweenness, and the bigger the more difference among all betweenness values. [41]
Centralization of stress centrality <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M16','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M16">View MathML</a> max(SC) is the maximal value of all stress centrality values and SCi represents the stress centrality of ith node. Finally this value is normalized by the theoretical maximum centralization score. It is close to 0 for a network where each node has the same stress centrality, and the bigger the more difference among all stress centrality values. [41]
Centralization of eigenvector centrality <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M17','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M17">View MathML</a> max(EC) is the maximal value of all eigenvector centrality values and ECi represents the eigenvector centrality of ith node. Finally this value is normalized by the theoretical maximum centralization score. It is close to 0 for a network where each node has the same eigenvector centrality, and the bigger the more difference among all eigenvector centrality values. [41]
Density <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M18','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M18">View MathML</a> l is the sum of total links and lexp is the number of possible links. It is closely related to the average connectivity. [41]
Average clustering coefficient <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M19','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M19">View MathML</a> <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M20','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M20">View MathML</a> is the clustering coefficient of node i. It is used to measure the extent of module structure present in a network. [36]
Transitivity <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M21','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M21">View MathML</a> li is the number of links between neighbors of node i and ki is the number of neighbors of node i. Sometimes it is also called the entire clustering coefficient. It has been shown to be a key structural property in social networks. [41]
Connectedness <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/113/mathml/M22','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/113/mathml/M22">View MathML</a> W is the number of pairs of nodes that are not reachable. It is one of the most important measurements for summarizing hierarchical structures. Con is 0 for graph without edges and is 1 for a connected graph. [42]

Deng et al.

Deng et al. BMC Bioinformatics 2012 13:113   doi:10.1186/1471-2105-13-113

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