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Fig. 1. Graph representation and graph analysis reveals regulatory patterns of cellular networks. The number of interactions a component participates in is quantified by its (in/out) degree, for example node O has both in-degree and out-degree 2. The clustering coefficient characterizes the cohesiveness of the neighborhood of a node - for example the clustering coefficient of I is 1, indicating that it is part of a three-node clique. The graph distance between two nodes is defined as the number of edges in the shortest path between them. For example, the distance between nodes P and O is 1, and the distance between nodes O and P is 2 (along the OQP path). The degree distribution P(k) [P(k_in) and P(k_out) in directed networks] quantifies the fraction of nodes with degree k, while the clustering-degree function C(k) gives the average clustering coefficient of nodes with degree k. (a) A linear pathway can be represented as a succession of directed edges connecting adjacent nodes. Because there are no shortcuts or feedbacks in a linear pathway, the distance between the starting node and end node increases linearly with the number of nodes. The in-degree and out-degree distribution indicates the existence of a source (k_in=0) and a sink (k_out=0) node. (b) This undirected and disconnected graph is composed of two connected components (EFGH and IJK), has a range of degrees from 1 to 3 and a range of clustering coefficients from 0 (for F) to 1 (for I, J and K). The connected component IJK is also a clique (completely connected subgraph) of three nodes. (c) This directed graph contains a feed-forward loop (MON) and a feedback loop (POQ), which is also the largest strongly connected component of the graph. The in-component of this graph contains L and M, while its out-component consists of the sink nodes N and R. The source node L can reach every other node in the network.

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