Fig. 1 Computing the four node TOMs for nodes A,B,C,D in two simple networks 1) tA,B,C,D=0+40+6=0.667 and 2) tA,B,C,D=1+41+6=0.714. From: Network neighborhood.

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Andy Yip, Steve Horvath Depts Human Genetics and Biostatistics, University of California, Los Angeles The Generalized Topological.

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Fig. 1 Computing the four node TOMs for nodes A,B,C,D in two simple networks 1) tA,B,C,D=0+40+6=0.667 and 2) tA,B,C,D=1+41+6=0.714. From: Network neighborhood analysis with the multi-node topological overlap measure Bioinformatics. 2006;23(2):222-231. doi:10.1093/bioinformatics/btl581 Bioinformatics | © 2006 The Author(s)This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 2 Using a local permutation test to choose the neighborhood size, i.e. the number of nodes S to be added to the initial neighborhood. (a) Yeast cell-cycle example; (b) Drosophila protein–protein interaction network. The solid line shows the MTOM values (y-axis) of the observed network as a function of different neighborhood sizes (x-axis). The dashed line shows the 95th percentile of the MTOM values based on locally permuted adjacency matrices. A local permutation only permutates those rows (and columns) of the adjacency matrix that correspond to node of the initial neighborhood. As heuristic, we suggest to choose a value for S close to where the solid line (observed values) crosses the dashed line (95th percentile of permuted values). From: Network neighborhood analysis with the multi-node topological overlap measure Bioinformatics. 2006;23(2):222-231. doi:10.1093/bioinformatics/btl581 Bioinformatics | © 2006 The Author(s)This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 8 Recursive MTOM neighborhoods contain a significantly better signal (y-axis) than averaged TOM neighborhoods. Here we report three representative examples: (a) the simulated network; (b) essential genes in the yeast PPI network; (c) essential genes in the Drosophila (fly) PPI network. We report the Kruskal–Wallis P-values for comparing the median values. The median value corresponds to the horizontal line inside the box. The corresponding notch around the median line denotes the 95% confidence interval. From: Network neighborhood analysis with the multi-node topological overlap measure Bioinformatics. 2006;23(2):222-231. doi:10.1093/bioinformatics/btl581 Bioinformatics | © 2006 The Author(s)This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 9 Recursive MTOM neighborhoods have higher MTOM values (y-axis) than averaged TOM neighborhoods. Here we report three representative examples: (a) the simulated network; (b) essential genes in the yeast PPI network; (c) essential genes in the Drosophila (fly) PPI network. From: Network neighborhood analysis with the multi-node topological overlap measure Bioinformatics. 2006;23(2):222-231. doi:10.1093/bioinformatics/btl581 Bioinformatics | © 2006 The Author(s)This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 7 Comparing the percentage of module 1 genes (y-axis) that are retrieved by different neighborhood construction methods for the simulated network. The recursive approach involving an initial neighborhood of two ‘hub’ genes in the first module leads to the best neighborhoods. In this application, the recursive and the non-recursive MTOM neighborhood analysis involving a single initial gene outperforms the naive approach of simply using the 30 genes with highest adjacency with the initial gene. Further, an initial neighborhood composed of two genes (with high topological overlap) leads to better results than initial neighborhoods composed of a single gene. From: Network neighborhood analysis with the multi-node topological overlap measure Bioinformatics. 2006;23(2):222-231. doi:10.1093/bioinformatics/btl581 Bioinformatics | © 2006 The Author(s)This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 3 Comparing the percentage of cell cycle proteins R (y-axis) in neighborhoods constructed in different ways for the Yeast Protein–Protein Physical Interaction Network (MIPS Data). The recursive approach involving an initial neighborhood of two cell cycle related ‘hub’ proteins performs better than approaches based on an initial set composed of a single protein. In this application, the recursive and the non-recursive MTOM neighborhood analysis involving a single initial protein do not lead to better results than the naive approach of building a neighborhood on the basis of direct connections (adjacency = 1) with the initial protein. We also report the P-values of the Kruskal–Wallis rank sum test, which is a non-parametric multi-group comparison test. From: Network neighborhood analysis with the multi-node topological overlap measure Bioinformatics. 2006;23(2):222-231. doi:10.1093/bioinformatics/btl581 Bioinformatics | © 2006 The Author(s)This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 4 Boxplots for visualizing the distribution of the topological overlap (y-axis) of initial protein pairs that lead to neighborhoods with a high percentage of cell cycle genes (x-axis). A boxplot consists of the most extreme values (the whiskers) in the dataset (maximum and minimum values), the lower and upper quartiles (lower and upper boundary of the box) and the median value (horizontal line inside the notch). A notch is drawn on each side of the box. If the notches of two plots do not overlap, the two medians differ significantly. From: Network neighborhood analysis with the multi-node topological overlap measure Bioinformatics. 2006;23(2):222-231. doi:10.1093/bioinformatics/btl581 Bioinformatics | © 2006 The Author(s)This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 5 Comparing the percentage of essential proteins R (y-axis) in neighborhoods constructed in different ways for the yeast PPI network (BioGrid Data). The neighborhoods initialized by sets of two or three hub proteins contain more essential proteins than those constructed from a single protein. We also report the P-values of the Kruskal–Wallis rank sum test, which is a standard non-parametric multi-group comparison test. From: Network neighborhood analysis with the multi-node topological overlap measure Bioinformatics. 2006;23(2):222-231. doi:10.1093/bioinformatics/btl581 Bioinformatics | © 2006 The Author(s)This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 6 Comparing the percentages of essential proteins R (y-axis) in neighborhoods constructed in the Drosophila PPI network. The recursive approach involving an initial neighborhood of a single essential protein performs better than the non-recursive and naive approaches. As the initial neighborhood size increases, so does the biological signal in the resulting neighborhoods. From: Network neighborhood analysis with the multi-node topological overlap measure Bioinformatics. 2006;23(2):222-231. doi:10.1093/bioinformatics/btl581 Bioinformatics | © 2006 The Author(s)This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 10 Recursive MTOM neighborhoods have higher average pairwise TOM value (y-axis) than averaged TOM neighborhoods. Here we report three representative examples: (a) the simulated network; (b) essential genes in the yeast PPI network; (c) essential genes in the Drosophila (fly) PPI network. From: Network neighborhood analysis with the multi-node topological overlap measure Bioinformatics. 2006;23(2):222-231. doi:10.1093/bioinformatics/btl581 Bioinformatics | © 2006 The Author(s)This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.