Local rewiring rules for evolving complex networks

ERC is grateful for the nancial support of the EPSRC

SOCIAL CAPITAL AND POVERTY REDUCTION: TOWARD A MATURE PARADIGM

Introduction The purposes of this paper are: (1) to introduce the social capital paradigm; (2) to present evidence that social capital has an important role in poverty reduction; and (3) to suggest several policy prescriptions for building and using social capital to reduce poverty. The social capital paradigm includes social capital, networks, socio-emotional goods, attachment values, institutions, and power. Social capital is a person or group's sympathy for others. Social capital resides in sympathetic relationships that can be described using networks. One reason to value social capital is because it can produce economic benefits and if neglected, economic disadvantages. Another reason to value social capital is because it can be used to produce socio-emotional goods. Sometimes socio-emotional goods become embedded in objects. When this occurs, the meaning and value of the object change. The change in the value of an object produced by embedded socio-emotional goods is the object's attachment value. Individuals exchange both physical and socio-emotional goods. Institutions are the rules that order and give meaning to exchanges. Institutions with high attachment values are more likely to be observed than those whose compliance depends on economic incentives or threats. Finally, power, the ability to influence others, depends on one's resources, including one's social capital. In most personalized transactions, persons exchange both socio-emotional goods and physical goods and services. Moreover, the relative amounts of socio-emotional goods and physical goods and services exchanged will alter the levels and terms of trade when measured in physical units. Since one's ability to include socio-emotional goods in exchanges for physical goods and services depends on one's social capital, the terms and levels of exchange of physical goods and services will be influenced by the transacting party's social capital. Those with high levels of social capital will have advantages over those who lack social capital because they can exchange both socio-emotional goods and physical goods and services. Furthermore, since social capital alters the terms and levels of trade and the terms and levels of trade influence the distribution of incomes derived from trades, then social capital also has an important influence on the distribution of household income and poverty. Some evidence suggests that the distribution of social capital in networks and the distribution of household incomes are connected.Food Security and Poverty, Institutional and Behavioral Economics,

Detecting rich-club ordering in complex networks

Uncovering the hidden regularities and organizational principles of networks arising in physical systems ranging from the molecular level to the scale of large communication infrastructures is the key issue for the understanding of their fabric and dynamical properties [1-5]. The ``rich-club'' phenomenon refers to the tendency of nodes with high centrality, the dominant elements of the system, to form tightly interconnected communities and it is one of the crucial properties accounting for the formation of dominant communities in both computer and social sciences [4-8]. Here we provide the analytical expression and the correct null models which allow for a quantitative discussion of the rich-club phenomenon. The presented analysis enables the measurement of the rich-club ordering and its relation with the function and dynamics of networks in examples drawn from the biological, social and technological domains.Comment: 1 table, 3 figure

Assortative Mixing Equilibria in Social Network Games

It is known that individuals in social networks tend to exhibit homophily (a.k.a. assortative mixing) in their social ties, which implies that they prefer bonding with others of their own kind. But what are the reasons for this phenomenon? Is it that such relations are more convenient and easier to maintain? Or are there also some more tangible benefits to be gained from this collective behaviour? The current work takes a game-theoretic perspective on this phenomenon, and studies the conditions under which different assortative mixing strategies lead to equilibrium in an evolving social network. We focus on a biased preferential attachment model where the strategy of each group (e.g., political or social minority) determines the level of bias of its members toward other group members and non-members. Our first result is that if the utility function that the group attempts to maximize is the degree centrality of the group, interpreted as the sum of degrees of the group members in the network, then the only strategy achieving Nash equilibrium is a perfect homophily, which implies that cooperation with other groups is harmful to this utility function. A second, and perhaps more surprising, result is that if a reward for inter-group cooperation is added to the utility function (e.g., externally enforced by an authority as a regulation), then there are only two possible equilibria, namely, perfect homophily or perfect heterophily, and it is possible to characterize their feasibility spaces. Interestingly, these results hold regardless of the minority-majority ratio in the population. We believe that these results, as well as the game-theoretic perspective presented herein, may contribute to a better understanding of the forces that shape the groups and communities of our society

Metrics for Graph Comparison: A Practitioner's Guide

Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees in data in these fields yields insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances (also known as $\lambda$ distances) and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies and different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and empirical datasets. We put forward a multi-scale picture of graph structure, in which the effect of global and local structure upon the distance measures is considered. We make recommendations on the applicability of different distance measures to empirical graph data problem based on this multi-scale view. Finally, we introduce the Python library NetComp which implements the graph distances used in this work

Generative models of the human connectome

The human connectome represents a network map of the brain's wiring diagram and the pattern into which its connections are organized is thought to play an important role in cognitive function. The generative rules that shape the topology of the human connectome remain incompletely understood. Earlier work in model organisms has suggested that wiring rules based on geometric relationships (distance) can account for many but likely not all topological features. Here we systematically explore a family of generative models of the human connectome that yield synthetic networks designed according to different wiring rules combining geometric and a broad range of topological factors. We find that a combination of geometric constraints with a homophilic attachment mechanism can create synthetic networks that closely match many topological characteristics of individual human connectomes, including features that were not included in the optimization of the generative model itself. We use these models to investigate a lifespan dataset and show that, with age, the model parameters undergo progressive changes, suggesting a rebalancing of the generative factors underlying the connectome across the lifespan.Comment: 38 pages, 5 figures + 19 supplemental figures, 1 tabl

A WHITE PAPER ON THE RELEVANCE OF SOCIAL CAPITAL FOR THE COLLEGE OF AGRICULTURE AND NATURAL RESOURCES (CANR)

Social capital is about relationships that are often based on earned or inherited kernels of commonality. Social capital raises the ethical question of when relationships should be allowed to influence outcomes. The essential theory underlying the social capital paradigm is that relationships of sympathy or social capital influence almost every interpersonal transaction. Since interpersonal transactions occur in many settings, the study of social capital is multi-disciplinary and interested in such diverse topics as charitable giving, leadership development, educational achievements, migration patterns, formation of cooperatives, how people care for the environment, diffusion of technology, advertising, economic development, family integrity, flow of legal, recreational, and health services, management of organizations, community development, animal health, passage of legislation, and the creation of civil society. Social capital is relevant to the College of Agriculture and Natural Resources (CANR) because it represents an important resource that must be studied and managed to achieve CANR's mission.Institutional and Behavioral Economics, Teaching/Communication/Extension/Profession,