Cell Systems Perspective Cross-Disciplinary Network Comparison : Matchmaking between Hairballs

Approach: Comparison Leverages Mathematical Formalism Let us first focus on the abstract association approach to biological networks, whose power lies in the simplicity of its formalism. A key point of comparison between various complex systems focuses on topology. The earliest and probably most important observation is that many networks organize themselves into scale-free architectures in which the majority of the nodes contain very few connections, while a few (also called ‘‘hubs’’) are highly connected (Box 1) (Barabasi and Albert, 1999). A surprising variety of networks exhibit scale-free architecture; for example, the Internet, air transport routes, and many social networks (Barabasi, 2003). Another important notion is that of a small-world network, in which any two nodes are, on average, separated by only a few steps (Box 1). Scale-free networks are also small-world networks because hubs ensure that the distance between any Box 1. Network Terminology Degree: The number of neighbors of a node. Scale-free networks: The degree distribution of the network is a statistical property that can be used to understand some of the organizing principles of the network. The degree distribution of a random network is a Poisson distribution. Most real-world networks, including biological networks, are organized in the form of scale-free networks that contain a small number of hubs that are highly connected in the network. The degree distribution in a scale-free network is better modeled as a power-law distribution. Hubs in a scale-free network also lead to the formation of small-world networks. Betweenness: The number of paths passing a node. Similar in spirit to heavily used bridges, highways, or intersections in transportation networks, a few centrally connected nodes funnel most of the paths between different parts of the network. High-betweenness nodes are referred to as ‘‘bottlenecks,’’ and the removal of these nodes could reduce the efficiency of communication between nodes (Newman, 2001). Small-world network: A small-world network is a kind of network in which the distance between nodes in the network is much smaller than the size of the network even though most nodes are not connected to one another. Typically, the average distance between any two nodes in a small-world network scales as the logarithm of the number of nodes in the network. Cliques: Cliques are defined as sub-networks in the graph that are completely connected, i.e., every pair of nodes in a clique contains an edge connecting them. Cliques form a single cohesive group in social networks, and such groups tend to act together. Similarly, a clique can be formed from a large biomolecular complex, such as a ribosome, that functions as a single unit. This property of cliques has been used to find missing edges to predict the function of biomolecules. Modules (community structure of networks): Most real-world networks can be divided into smaller modules that have a large density of internal edges but relatively fewer edges that connect nodes from different modules. For instance, social networks tend to have communities within them due to the relatively larger number of interactions between people in the same neighborhood, school, or workplace. Similarly, in a biological context, a large number of biological components can form a single functional macromolecular complex, such as the ribosome. Awide variety ofmethods have been developed to uncover themodular structure of networks. Most of thesemethods are based on optimizing themodularity of the network that compares the number of intraand inter-module links within the network. PageRank algorithm: PageRank is a prominent example of measuring the importance of a node by taking into account the importance of its neighbors. Originally developed in social network analysis (Katz, 1953), PageRank utilizes an algorithm developed to rank relevant documents based on the rank of thewebsites that link to this document in a self-consistentmanner—i.e., being linked to by higher-ranking nodes has a larger impact on the document’s ranking. This algorithm has been applied to food webs to prioritize species that are in danger of extinction (Allesina and Pascual, 2009) and has also been used to rank marker genes and predict clinical outcome for cancers (Winter et al., 2012). Cell Systems