Table 1S:

Listing and explanation of 14 node-related and 3 node pair-related network properties. See for example (Estrada 2006)1 and (Freeman 1979)2.

Property name / Definition / description
Eccentricity / / The maximum graph distance d(v,w)between nodev and any other nodew in a networkT.
Betweeness centrality / / A measure of the number of shortest paths between all node pairs, to which nodev belongs. σ(u,w,v) is the number of shortest paths between nodesu and w passing through nodev andσ(u,w) is the number of shortest paths between u and w.
Degree centrality / / The number of edges or incident nodes of nodev, denoted as ev.
Closeness centrality / / The mean shortest path between nodev and all other nodes. n is the number of nodes in the network.
Information centrality / / The amount of information that can be transmitted between nodev and all other nodes, calculated as the harmonic mean distance between all paths between v and all other nodes. ivw is the sum of reciprocal distances for all paths between nodesv and w. e is the number of edges in the network.
Subgraph centrality / / The participation of vertex v in all subgraphs of the network. μk(v) is the number of closed walks of length k starting and ending at nodev.
Bipartivity / / The extent to which nodev contributes to the global bipartivity of the network, calculated as the ratio of even to total closed walks starting and ending at nodev.
Biconnected components / / Specifies whether removal of nodev would disconnect the network such that vertices previously connected to each other are no longer connected. ap(T) is the set of articulation points of the networkT.
Clustering coefficient / / A measure of the connectedness of the neighborhood of nodev, calculated as the number of edges in the neighborhood of v divided by the total possible number of edges in the neighborhood. This measures how close the neighborhood is to being a clique. ek(v) is the set of edges connecting between any two nodes in the neighborhood of nodev.
Core numbers / / A measure of how well connected is the subgraph to which nodev belongs. The core number of nodev is the largest integer c such that v still exists in the subgraph generated by removing all nodes of degree less than c.
Prestige / / A measure of the importance of the neighbors of nodev, calculated as the average degree of the neighbors of v.
Eigenvector centrality / / A measure of the global importance of a node in the graph, calculated as the nodes principal eigenvector of the adjacency matrix for the network. eig1(v) is the vth element in the principal eigenvector.
Node size / / The molecular count of the node normalized by the Euclidean norm of the most frequent compotype in wild time.
Large node distance / / The minimum graph theoretic distance between nodev and any node with large node size. A large node is defined as any node with node size more than one positive standard deviation away from the mean node size.
Distance / Dij=d(v,w) / The graph theoretic shortest path distance between the two nodes v and w in the network (only for node pairs).
Catalytic out similarity / / The number of neighbors connected by outgoing edges common to both nodes v and w divided by the total number of such neighbors (only for pairs).
Catalytic in similarity / / The number of neighbors connected by incoming edges common to both nodes v and w divided by the total number of such neighbors (only for pairs).

1 Estrada E (2006) Protein bipartivity and essentiality in the yeast protein-protein interaction network. J Proteome Res 5:2177-84

2 Freeman LC (1979) Centrality in Social Networks: Coneceptual Clarification. Social Networks 1:215-239

Table 2S: A mathematical formulation of the fitness measures used in this study.H(v1,v2)isthe scalar product between vectors v1 and v2. CWjisthe jth most frequent compotype in the wild type and CMjisthe jth most frequent compotype in the mutant. CMWisthe mutant compotype which maximizes the value of H(CW1,CMj), i.e. the mutant compotype most similar to the most frequent wild type compotype. R(C)isthe frequency in number of generations compotype C.

fitness measure / formula / description
H / / The scalar product between the most frequent compotype in the wild type and the compotype in the mutant that is most similar to it.
H’ / / Fitness H adjusted by the number of generations of the most similar compotype in the mutant divided by the number of generations of the most frequent compotype in the wild type
G / GW / GM / The ratio ofgrowth times of the wild type mutant the mutant, each measured as the sum of the durations of all join/leave events over all generations
J / JW / JM / The ratio of the number of combined join and leaveevents between the wild type and the mutant

Fig. 1S: Distribution of fitness measures in GARD analysis with NG=30:H (A), W (B) and G(C).Note that H by definition can not be more than 1 (see Methods).


Fig. 2S:Absolute Pearson correlation between network properties and the four measures of fitness used in this work. Two datasets are shown; A) repertoiresize NG=30. B) repertoire size NG=100. The network properties are (in order of increasing correlation): 1.closeness centrality, 2.clustering coefficient, 3.primary eigenvector, 4.bipartivity, 5.subgraph centrality, 6.betweenness centrality, 7.eccentricity, 8.is biconnected, 9.information centrality, 10.core numbers, 11.prestige, 12.degree centrality, 13.large node distance, 14.node size. (See Table 1S for definitions).The four fitness measures used were H,(blue);H’, light blue;, G, yellow; J, brown.


Fig. 3S: Correlation between selected network properties and lethality in a data set of 1000 different GARD networks of size NG=100. The shown network properties are as in Fig. 6.


Fig. 4S: A. Correlation of the lack of synthetic lethality (Brown squares) and the occurrence of synthetic lethality (green diamonds) to “catalyst similarity” (Catalytic out similarity, Table 1S).B.The same, for “substrate similarity” (Catalytic out similarity, Table 1S). Note the different scale for the two y-axes.


Figure 5S: The same analysis as in Fig. 2, performed for NG=100. The best linear fit (R=-0.98) gave P(X) ~ X-2.1