Effects of random rewiring on the degree correlation of scale-free networks

Framework for converting mechanistic network models to probabilistic models

There are two prominent paradigms for the modelling of networks: in the first, referred to as the mechanistic approach, one specifies a set of domain-specific mechanistic rules that are used to grow or evolve the network over time; in the second, referred to as the probabilistic approach, one describes a model that specifies the likelihood of observing a given network. Mechanistic models (models developed based on the mechanistic approach) are appealing because they capture scientific processes that are believed to be responsible for network generation; however, they do not easily lend themselves to the use of inferential techniques when compared with probabilistic models. We introduce a general framework for converting a mechanistic network model (MNM) to a probabilistic network model (PNM). The proposed framework makes it possible to identify the essential network properties and their joint probability distribution for some MNMs; doing so makes it possible to address questions such as whether two different mechanistic models generate networks with identical distributions of properties, or whether a network property, such as clustering, is over- or under-represented in the networks generated by the model of interest compared with a reference model. The proposed framework is intended to bridge some of the gap that currently exists between the formulation and representation of mechanistic and PNMs. We also highlight limitations of PNMs that need to be addressed in order to close this gap.

Measuring the variability of local characteristics in complex networks: Empirical and analytical analysis

We examine the dynamics for the average degree of a node's neighbors in complex networks. It is a Markov stochastic process, and at each moment of time, this quantity takes on its values in accordance with some probability distribution. We are interested in some characteristics of this distribution: its expectation and its variance, as well as its coefficient of variation. First, we look at several real communities to understand how these values change over time in social networks. The empirical analysis of the behavior of these quantities for real networks shows that the coefficient of variation remains at high level as the network grows. This means that the standard deviation and the mean degree of the neighbors are comparable. Then, we examine the evolution of these three quantities over time for networks obtained as simulations of one of the well-known varieties of the Barabási-Albert model, the growth model with nonlinear preferential attachment (NPA) and a fixed number of attached links at each iteration. We analytically show that the coefficient of variation for the average degree of a node's neighbors tends to zero in such networks (albeit very slowly). Thus, we establish that the behavior of the average degree of neighbors in Barabási-Albert networks differs from its behavior in real networks. In this regard, we propose a model based on the NPA mechanism with the rule of random number of edges added at each iteration in which the dynamics of the average degree of neighbors is comparable to its dynamics in real networks.

Autopoietic Influence Hierarchies in Pancreatic β Cells

β cells are biologically essential for humans and other vertebrates. Because their functionality arises from cell-cell interactions, they are also a model system for collective organization among cells. There are currently two contradictory pictures of this organization: the hub-cell idea pointing at leaders who coordinate the others, and the electrophysiological theory describing all cells as equal. We use new data and computational modeling to reconcile these pictures. We find via a network representation of interacting β cells that leaders emerge naturally (confirming the hub-cell idea), yet all cells can take the hub role following a perturbation (in line with electrophysiology).

Dynamics of the Global Wheat Trade Network and Resilience to Shocks

Agri-food trade networks are increasingly vital to human well-being in a globalising world. Models can help us gain insights into trade network dynamics and predict how they might respond to future disturbances such as extreme weather events. Here we develop a preferential attachment (PA) network model of the global wheat trade network. We find that the PA model can replicate the time evolution of crucial wheat trade network metrics from 1986 to 2011. We use the calibrated PA model to predict the response of wheat trade network metrics to shocks of differing length and severity, including both attacks (outward edge removal on high degree nodes) and errors (outward edge removal on randomly selected nodes). We predict that the network will become less vulnerable to attacks but will continue to exhibit low resilience until 2050. Even short-term shocks strongly increase link diversity and cause long-term structural changes that influence the network's response to subsequent shocks. Attacks have a greater impact than errors. However, with repeated attacks, each attack has a lesser impact than the previous attack. We conclude that dynamic models of multi-annual, commodity-specific networks should be further developed to gain insight into possible futures of global agri-food trade networks.