Evolutionary dynamics on any population structure.

Evolution occurs in populations of reproducing individuals. The structure of a population can affect which traits evolve. Understanding evolutionary game dynamics in structured populations remains difficult. Mathematical results are known for special structures in which all individuals have the same number of neighbours. The general case, in which the number of neighbours can vary, has remained open. For arbitrary selection intensity, the problem is in a computational complexity class that suggests there is no efficient algorithm. Whether a simple solution for weak selection exists has remained unanswered. Here we provide a solution for weak selection that applies to any graph or network. Our method relies on calculating the coalescence times of random walks. We evaluate large numbers of diverse population structures for their propensity to favour cooperation. We study how small changes in population structure-graph surgery-affect evolutionary outcomes. We find that cooperation flourishes most in societies that are based on strong pairwise ties.

Evolution of cooperation on large networks with community structure.

Cooperation is a major factor in the evolution of human societies. The structure of social networks, which affects the dynamics of cooperation and other interpersonal phenomena, have common structural signatures. One of these signatures is the tendency to organize as groups. This tendency gives rise to networks with community structure, which are composed of distinct modules. In this paper, we study analytically the evolutionary game dynamics on large modular networks in the limit of weak selection. We obtain novel analytical conditions such that natural selection favours cooperation over defection. We calculate the transition point for each community to favour cooperation. We find that a critical inter-community link creation probability exists for given group density, such that the overall network supports cooperation even if individual communities inhibit it. As a byproduct, we present solutions for the critical benefit-to-cost ratio which perform with remarkable accuracy for diverse generative network models, including those with community structure and heavy-tailed degree distributions. We also demonstrate the generalizability of the results to arbitrary two-player games.

Conjoining uncooperative societies facilitates evolution of cooperation.

Social structure affects the emergence and maintenance of cooperation. Here, we study the evolutionary dynamics of cooperation in fragmented societies, and show that conjoining segregated cooperation-inhibiting groups, if done properly, rescues the fate of collective cooperation. We highlight the essential role of intergroup ties, which sew the patches of the social network together and facilitate cooperation. We point out several examples of this phenomenon in actual settings. We explore random and non-random graphs, as well as empirical networks. In many cases, we find a marked reduction of the critical benefit-to-cost ratio needed for sustaining cooperation. Our finding gives hope that the increasing worldwide connectivity, if managed properly, can promote global cooperation.

Statistical methods for constructing disease comorbidity networks from longitudinal inpatient data.

Tools from network science can be utilized to study relations between diseases. Different studies focus on different types of inter-disease linkages. One of them is the comorbidity patterns derived from large-scale longitudinal data of hospital discharge records. Researchers seek to describe comorbidity relations as a network to characterize pathways of disease progressions and to predict future risks. The first step in such studies is the construction of the network itself, which subsequent analyses rest upon. There are different ways to build such a network. In this paper, we provide an overview of several existing statistical approaches in network science applicable to weighted directed networks. We discuss the differences between the null models that these models assume and their applications. We apply these methods to the inpatient data of approximately one million people, spanning approximately 17 years, pertaining to the Montreal Census Metropolitan Area. We discuss the differences in the structure of the networks built by different methods, and different features of the comorbidity relations that they extract. We also present several example applications of these methods.

Effect of node attributes on the temporal dynamics of network structure.

Many natural and social networks evolve in time and their structures are dynamic. In most networks, nodes are heterogeneous, and their roles in the evolution of structure differ. This paper focuses on the role of individual attributes on the temporal dynamics of network structure. We focus on a basic model for growing networks that incorporates node attributes (which we call "quality"), and we focus on the problem of forecasting the structural properties of the network in arbitrary times for an arbitrary initial network. That is, we address the following question: If we are given a certain initial network with given arbitrary structure and known node attributes, then how does the structure change in time as new nodes with given distribution of attributes join the network? We solve the model analytically and obtain the quality-degree joint distribution and degree correlations. We characterize the role of individual attributes in the position of individual nodes in the hierarchy of connections. We confirm the theoretical findings with Monte Carlo simulations.

Qualities and Inequalities in Online Social Networks through the Lens of the Generalized Friendship Paradox.

The friendship paradox is the phenomenon that in social networks, people on average have fewer friends than their friends do. The generalized friendship paradox is an extension to attributes other than the number of friends. The friendship paradox and its generalized version have gathered recent attention due to the information they provide about network structure and local inequalities. In this paper, we propose several measures of nodal qualities which capture different aspects of their activities and influence in online social networks. Using these measures we analyse the prevalence of the generalized friendship paradox over Twitter and we report high levels of prevalence (up to over 90% of nodes). We contend that this prevalence of the friendship paradox and its generalized version arise because of the hierarchical nature of the connections in the network. This hierarchy is nested as opposed to being star-like. We conclude that these paradoxes are collective phenomena not created merely by a minority of well-connected or high-attribute nodes. Moreover, our results show that a large fraction of individuals can experience the generalized friendship paradox even in the absence of a significant correlation between degrees and attributes.

Growing multiplex networks with arbitrary number of layers.

This paper focuses on the problem of growing multiplex networks. Currently, the results on the joint degree distribution of growing multiplex networks present in the literature pertain to the case of two layers and are confined to the special case of homogeneous growth and are limited to the state state (that is, the limit of infinite size). In the present paper, we first obtain closed-form solutions for the joint degree distribution of heterogeneously growing multiplex networks with arbitrary number of layers in the steady state. Heterogeneous growth means that each incoming node establishes different numbers of links in different layers. We consider both uniform and preferential growth. We then extend the analysis of the uniform growth mechanism to arbitrary times. We obtain a closed-form solution for the time-dependent joint degree distribution of a growing multiplex network with arbitrary initial conditions. Throughout, theoretical findings are corroborated with Monte Carlo simulations. The results shed light on the effects of the initial network on the transient dynamics of growing multiplex networks and takes a step towards characterizing the temporal variations of the connectivity of growing multiplex networks, as well as predicting their future structural properties.