Patent records and collaboration networks used in this paper.

The collaboration networks at the inventor and company levels were constructed from the Japan and U.S. patent records of several decades, with number of patents denoted by NP. For each collaboration network we show the number of nodes (N), edges (L), mean degree (⟨k⟩ = 2L/N), relative size of the largest connected component (slc = Nlc/N, where Nlc is the number of nodes in the largest connected component), fraction of isolated nodes (n0), clustering coefficient (C) and degree correlation (r). In graph theory, the connected components of a graph G are the set of largest subgraphs of G that are each connected (i.e., any two vertices or nodes in a connected component are connected to each other by paths), which can be easily computed using either breadth-first search or depth-first search. The largest connected component (often referred to as the giant component) is the connected component of the largest size (number of nodes). The clustering coefficient C of a graph is a measure of the degree to which the nodes in the graph tend to cluster together (i.e., form triangles) [23]. C can be calculated as (3 × number of triangles)/(number of connected triples). The degree correlation r of a network is given by the Pearson correlation coefficient of degrees between pairs of linked nodes [24].