Minimum shortest path length is the minimum of the lengths of shortest paths between every pair of candidate genes (or every pair of candidate and target genes).
Average shortest path length, is the average of the lengths of shortest paths between every pair of candidate genes (or every pair of candidate and target genes).
In order to construct a subnetwork in which all genes associated with EH are connected directly or indirectly with minimum number of nodes, we found out all shortest paths between every pair of candidate genes.
Specifically, (P_{q}={{p_{q}^{1}}, {p_{q}^{2}}, ldots p_{q}^{|P_{q}|} }) is a set of candidate paths for q sorted in increasing path length order.
The value of new_links_number for each of candidate path of L S P 2 can be found by counting the links that are not included in the Links used column.
Friends said Mr. Romney could not imagine following the well-worn path of defeated Republican candidates to Fox News.
Each cell of Table 2 contains the links of candidate paths that belong to other requests; e.g., the second candidate path of L S P 2, ({p^{2}_{2}}) is [ R4,R3,R2] and its links are R4−R3 and R3−R2.
Then, by the use of Newton gravity theory and a special shortest-path procedure, a set of candidate routes is formed, categorized by hierarchy (mass, feeder, local routes).
The evacuation paths, location and area of candidate shelters, and community location data were extracted using ArcGIS software 10.0 (ESRI 2010) from the map of Beijing City published by China Cartographic Publishing House in 2011 (Fig. 1a), and the population of communities was provided by the Beijing Bureau of Civil Affairs in 2010 (Fig. 1b).
Our contribution consists in quantifying (1) the effects the selection of candidate paths per node pair has on the restoration ratio, (2) the effect of restoration schemes on the restoration ratio, (3) the effect of failure scenarios on the restoration ratio, and finally (4) the effect of network connectivity on the restoration ratio.
