## Astronomy Journals – Network Properties

Articles form a graph where the edges represent a relationship between the articles. With some of those relationships, the graph will be a directed graph. The relationship “X cites Y” is an example. Representing articles as a graph allows us to do a number of interesting observations. Can we detect clustering within the graph? I will discuss this at a later time. Another question is: how does the topology of the graph change over time? More specifically: can we detect densification? Does the number of edges increase? The diagram below compares the number of nodes (=articles) with the number of edges (=references) for the major astronomy journals in the time period of 1980 through 2006. Citations to articles outside the network (temporally or to other journals, not in the network) were disregarded.

The function fitted to this relationship is

e(t) = a×n(t)^{b}

to illustrate the power law form for network densification. In this relation e(t) represents the number of edges at time t, and n(t) is the number of nodes. An exponent of 1 would indicate linear growth. The fit results in an exponent of about 1.9 (with a correlation of 0.99), indicating high densification over time, i.e. non-linear growth. Another implication is that in an average sense, bibliographies have increased in length over time.