## Table 1 |
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The network topological indexes used in this study |
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Indexes |
Formula |
Explanation |
Note |
Ref |

Part I: network indexes for individual nodes |
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Connectivity | 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 | 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 i^{th} node. High Stress node can serve as a broker. |
[34] | |

Betweenness | is the total number of shortest paths between j and k. |
It is used to desibe the ratio of paths that pass through the i^{th} node. High Betweenness node can serve as a broker similar to stress centrality. |
[34] | |

Eigenvector centrality | M(i) is the set of nodes that are connected to the i^{th} 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 | l_{i} is the number of links between neighbors of node i and k_{i}’ 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 | E is the global efficiency and E_{i} 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 |
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Average connectivity | k_{i} is degree of node i and n is the number of nodes. |
Higher avgK means a more complex network. |
[39] | |

Average geodesic distance | d_{ij} is the shortest path between node i and j. |
A smaller GD means all the nodes in the network are closer. |
[39] | |

Geodesic efficiency | all parameters shown above. | It is the opposite of GD. A higher E means that the nodes are closer. |
[40] | |

Harmonic geodesic distance | E is geodesic efficiency. |
The reciprocal of E, which is similar to GD but more appropriate for disjoint graph. |
[40] | |

Centralization of degree | max(k) is the maximal value of all connectivity values and k_{i} represents the connectivity of i^{th} 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 | max(B) is the maximal value of all betweenness values and B_{i} represents the betweenness of i^{th} 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 | max(SC) is the maximal value of all stress centrality values and SC_{i} represents the stress centrality of i^{th} 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 | max(EC) is the maximal value of all eigenvector centrality values and EC_{i} represents the eigenvector centrality of i^{th} 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 | l is the sum of total links and l_{exp} is the number of possible links. |
It is closely related to the average connectivity. | [41] | |

Average clustering coefficient | is the clustering coefficient of node i. |
It is used to measure the extent of module structure present in a network. | [36] | |

Transitivity | l_{i} is the number of links between neighbors of node i and k_{i}’ 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 | 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