Table 1 Graph metrics reduce structural properties of network to (vectors of) real numbers, facilitating the comparison of different networks

The statistical distribution followed by the degrees of the nodes in a network. Many real-world networks have degree distributions that depart sharply from those of classical random network models (Table 1).

In an unweighted graph G, the shortest path between nodes u and v is the minimum number of links one must traverse to move from u to v. If G is weighted, the shortest path is that with the minimal sum of link weights. The average shortest path or characteristic path length is the average length of all shortest paths (between all node pairs) in a network.

A centrality metric gives a ranking of nodes according to their “importance”. The simplest measure is degree centrality – the degree of a node specifies its importance. Closeness centrality is the reciprocal of the sum of the shortest paths to all other nodes (i.e. a node whose closeness centrality is high is close to many nodes). Betweenness centrality is the fraction of shortest paths passing through a node. Eigenvector centrality and Pagerank are measures of how frequently one arrives at a node when performing a random walk on a network.