Asymmetric access to information impacts the power-law exponent in networks

The preferential attachment (PA) process is a popular theory for explaining network power-law degree distributions. In PA, the probability that a new vertex adds an edge to an existing vertex depends on the connectivity of the target vertex. In real-world networks, however, each vertex may have asymmetric accessibility to information. Here we address this issue using a new network-generation mechanism that incorporates asymmetric accessibility to upstream and downstream information. We show that this asymmetric information accessibility directly affects the power-law exponent, producing a broad range of values that are consistent with observations. Our findings shed new light on the possible mechanisms in three important real-world networks: a citation network, a hyperlink network, and an online social network.

Generalized Gelation Theory describes Human Online Aggregation in support of Extremism

Though many aggregation theories exist for physical, chemical and biological systems, they do not account for the significant heterogeneity found, for example, in populations of living objects. This is unfortunate since understanding how heterogeneous individuals come together in support of an extremist cause, for example, represents an urgent societal problem. Here we develop such a theory and show that the intrinsic population heterogeneity can significantly delay the gel transition point and change the gels growth rate. We apply our theory to examine how humans aggregate online in support of a particular extremist cause. We show that the theory provides an accurate description of the online extremist support for ISIS (so-called Islamic State) which started in late 2014.