Coexistence of opposite opinions in a network with communities

The Majority Rule is applied to a topology that consists of two coupled random networks, thereby mimicking the modular structure observed in social networks. We calculate analytically the asymptotic behaviour of the model and derive a phase diagram that depends on the frequency of random opinion flips and on the inter-connectivity between the two communities. It is shown that three regimes may take place: a disordered regime, where no collective phenomena takes place; a symmetric regime, where the nodes in both communities reach the same average opinion; an asymmetric regime, where the nodes in each community reach an opposite average opinion. The transition from the asymmetric regime to the symmetric regime is shown to be discontinuous.Comment: 14 pages, 4 figure

Community Structure in the United States House of Representatives

We investigate the networks of committee and subcommittee assignments in the United States House of Representatives from the 101st--108th Congresses, with committees connected according to ``interlocks'' or common membership. We examine the House's community structure using several methods, which reveal strong links between different committees as well as the intrinsic hierarchical structure within the House as a whole. We identify structural changes, including additional hierarchical levels and higher modularity, resulting from the 1994 elections, in which the Republican party earned majority status in the House for the first time in more than forty years. We also combine our network approach with analysis of roll call votes using singular value decomposition to uncover correlations between the political and organizational structure of House committees