Cosponsorship Network Analysis

Cosponsorship is a meaningful but imperfect signal. It is costless and public, so legislators use it both to genuinely collaborate on legislation and to take symbolic positions for constituents or interest groups — signing on without any working relationship. Network analysis treats it as a behavioral trace of political proximity, and Fowler's weighting reduces the influence of mass-signed, low-information bills. But analysts should remember that a tie blends real collaboration with position-taking, validate findings against other measures, and frame conclusions accordingly rather than equating every cosponsorship with substantive teamwork.

Because network ties are interdependent: whether two legislators connect depends on the rest of the network — shared partners, popularity, clustering — which violates the independence assumption underlying ordinary regression on dyads. Treating each potential tie as an independent observation biases standard errors and can mislead about what drives connection. Exponential random graph models, as Cranmer and Desmarais argue, model the whole network's probability as a function of structural terms and covariates, properly accounting for this interdependence, so they are the appropriate tool for inference about tie formation rather than mere description.

Start from the bipartite incidence matrix B with legislators in rows and bills in columns, where an entry marks sponsorship or cosponsorship. Multiplying B by its transpose projects this two-mode data onto a one-mode legislator network whose entries count shared bills; you then remove the diagonal and apply an edge-weighting scheme — such as dividing each bill's contribution among its cosponsors — to keep large bills from dominating. The result is a weighted (and, if you preserve sponsor-versus-cosponsor direction, directed) network ready for centrality, community, and ERGM analysis. In R this projection and weighting are straightforward with igraph or statnet.