A classical model for social-influence-driven opinion change is the threshold model. Here we study cascades of opinion change driven by threshold model dynamics in the case where multiple initiators trigger the cascade, and where all nodes possess the same adoption threshold ϕ. Specifically, using empirical and stylized models of social networks, we study cascade size as a function of the initiator fraction p. We find that even for arbitrarily high value of ϕ, there exists a critical initiator fraction pc(ϕ) beyond which the cascade becomes global. Network structure, in particular clustering, plays a significant role in this scenario. Similarly to the case of single-node or single-clique initiators studied previously, we observe that community structure within the network facilitates opinion spread to a larger extent than a homogeneous random network. Finally, we study the efficacy of different initiator selection strategies on the size of the cascade and the cascade window.

Social networks are not static but, rather, constantly evolve in time. One of the elements thought to drive the evolution of social network structure is homophily-the need for individuals to connect with others who are similar to them. In this paper, we study how the spread of a new opinion, idea, or behavior on such a homophily-driven social network is affected by the changing network structure. In particular, using simulations, we study a variant of the Axelrod model on a network with a homophily-driven rewiring rule imposed. First, we find that the presence of rewiring within the network, in general, impedes the reaching of consensus in opinion, as the time to reach consensus diverges exponentially with network size N. We then investigate whether the introduction of committed individuals who are rigid in their opinion on a particular issue can speed up the convergence to consensus on that issue. We demonstrate that as committed agents are added, beyond a critical value of the committed fraction, the consensus time growth becomes logarithmic in network size N. Furthermore, we show that slight changes in the interaction rule can produce strikingly different results in the scaling behavior of consensus time, T(c). However, the benefit gained by introducing committed agents is qualitatively preserved across all the interaction rules we consider.

We study a three-state (leftist, rightist, centrist) model that couples the dynamics of social balance with an external deradicalizing field. The mean-field analysis shows that there exists a critical value of the external field p_{c} such that for a weak external field (pp_{c}), there is only one (stable) fixed point, which corresponds to an all-centrist consensus state (absorbing state). In the weak-field regime, the convergence time to the absorbing state is evaluated using the quasistationary distribution and is found to be in agreement with the results obtained by numerical simulations.

Modularity, since its introduction, has remained one of the most widely used metrics to assess the quality of community structure in a complex network. However the resolution limit problem associated with modularity limits its applicability to networks with community sizes smaller than a certain scale. In the past various attempts have been made to solve this problem. More recently a new metric, modularity density, was introduced for the quality of community structure in networks in order to solve some of the known problems with modularity, particularly the resolution limit problem. Modularity density resolves some communities which are otherwise undetectable using modularity. However, we find that it does not solve the resolution limit problem completely by investigating some cases where it fails to detect expected community structures. To address this problem, we introduce a variant of this metric and show that it further reduces the resolution limit problem, effectively eliminating the problem in a wide range of networks.

We introduce an ensemble learning scheme for community detection in complex networks. The scheme uses a Machine Learning algorithmic paradigm we call Extremal Ensemble Learning. It uses iterative extremal updating of an ensemble of network partitions, which can be found by a conventional base algorithm, to find a node partition that maximizes modularity. At each iteration, core groups of nodes that are in the same community in every ensemble partition are identified and used to form a reduced network. Partitions of the reduced network are then found and used to update the ensemble. The smaller size of the reduced network makes the scheme efficient. We use the scheme to analyze the community structure in a set of commonly studied benchmark networks and find that it outperforms all other known methods for finding the partition with maximum modularity.