Reciprocity in Social Networks with Capacity Constraints

Directed links -- representing asymmetric social ties or interactions (e.g., "follower-followee") -- arise naturally in many social networks and other complex networks, giving rise to directed graphs (or digraphs) as basic topological models for these networks. Reciprocity, defined for a digraph as the percentage of edges with a reciprocal edge, is a key metric that has been used in the literature to compare different directed networks and provide "hints" about their structural properties: for example, are reciprocal edges generated randomly by chance or are there other processes driving their generation? In this paper we study the problem of maximizing achievable reciprocity for an ensemble of digraphs with the same prescribed in- and out-degree sequences. We show that the maximum reciprocity hinges crucially on the in- and out-degree sequences, which may be intuitively interpreted as constraints on some "social capacities" of nodes and impose fundamental limits on achievable reciprocity. We show that it is NP-complete to decide the achievability of a simple upper bound on maximum reciprocity, and provide conditions for achieving it. We demonstrate that many real networks exhibit reciprocities surprisingly close to the upper bound, which implies that users in these social networks are in a sense more "social" than suggested by the empirical reciprocity alone in that they are more willing to reciprocate, subject to their "social capacity" constraints. We find some surprising linear relationships between empirical reciprocity and the bound. We also show that a particular type of small network motifs that we call 3-paths are the major source of loss in reciprocity for real networks

Reciprocity in Social Networks with Capacity Constraints

ABSTRACT Directed links -representing asymmetric social ties or interactions (e.g., "follower-followee") -arise naturally in many social networks and other complex networks, giving rise to directed graphs (or digraphs) as basic topological models for these networks. Reciprocity, defined for a digraph as the percentage of edges with a reciprocal edge, is a key metric that has been used in the literature to compare different directed networks and provide "hints" about their structural properties: for example, are reciprocal edges generated randomly by chance or are there other processes driving their generation? In this paper we study the problem of maximizing achievable reciprocity for an ensemble of digraphs with the same prescribed in-and out-degree sequences. We show that the maximum reciprocity hinges crucially on the in-and outdegree sequences, which may be intuitively interpreted as constraints on some "social capacities" of nodes and impose fundamental limits on achievable reciprocity. We show that it is NP-complete to decide the achievability of a simple upper bound on maximum reciprocity, and provide conditions for achieving it. We demonstrate that many real networks exhibit reciprocities surprisingly close to the upper bound, which implies that users in these social networks are in a sense more "social" than suggested by the empirical reciprocity alone in that they are more willing to reciprocate, subject to their "social capacity" constraints. We find some surprising linear relationships between empirical reciprocity and the bound. We also show that a particular type of small network motifs that we call 3-paths are the major source of loss in reciprocity for real networks

Human neuromaturation, juvenile extreme energy liability, and adult cognition/cooperation

Human childhood and adolescence is the period in which adult cognitive competences (including those that create the unique cooperativeness of humans) are acquired. It is also a period when neural development puts a juvenile’s survival at risk due to the high vulnerability of their brain to energy shortage. The brain of a 4 year-old human uses ≈50% of its total energy expenditure (TEE) (cf. adult ≈12%). This brain expensiveness is due to (1) the brain making up ≈6% of a 4 year-old body compared to 2% in an adult, and (2) increased energy metabolism that is ≈100% greater in the gray matter of a child than in an adult (a result of the extra costs of synaptic neuromaturation). The high absolute number of neurons in the human brain requires as part of learning a prolonged neurodevelopment. This refines inter- and intraarea neural networks so they become structured with economical “small world” connectivity attributes (such as hub organization and high cross-brain differentiation/integration). Once acquired, this connectivity enables highly complex adult cognitive capacities. Humans evolved as hunter-gatherers. Contemporary hunter-gatherers (and it is also likely Middle Paleolithic ones) pool high energy foods in an egalitarian manner that reliably supported mothers and juveniles with high energy intake. This type of sharing unique to humans protects against energy shortage happening to the immature brain. This cooperation that protects neuromaturation arises from adults having the capacity to communicate and evaluate social reputation, cognitive skills that exist as a result of extended neuromaturation. Human biology is therefore characterized by a presently overlooked bioenergetic-cognition loop (called here the “HEBE ring”) by which extended neuromaturation creates the cooperative abilities in adults that support juveniles through the potentially vulnerable period of the neurodevelopment needed to become such adults

Desistance, reflexivity and relationality : a case study

This paper presents the analysis of a single life-story drawn from a larger study examining theindividual, relational and structural contributions to the desistance process. The emphasis here is on the contributions of key social relations in ‘Evan’s’ narrative of change. How people relate to one another, and what these relationships mean to them both as individuals and together, are critical aspects of understanding the role of social relations in desistance. This paper concludes by considering how penal practices might generate and sustain the kinds of social capital and reflexive, relational networks relevant to desistance

Evolution of Human-like Social Grooming Strategies regarding Richness and Group Size

Human beings tend to cooperate with close friends, therefore they have to construct strong social relationships to recieve cooperation from others. Therefore they should have acquired their strategies of social relationship construction through an evolutionary process. The behavior of social relationship construction is know as "social grooming." In this paper, we show that there are four classes including a human-like strategy in evolutionary dynamics of social grooming strategies based on an evolutionary game simulation. Social relationship strengths (as measured by frequency of social grooming) often show a much skewed distribution (a power law distribution). It may be due to time costs constraints on social grooming, because the costs are too large to ignore for having many strong social relationships. Evolution of humans' strategies of construction of social relationships may explain the origin of human intelligence based on a social brain hypothesis. We constructed an individual-based model to explore the evolutionary dynamics of social grooming strategies. The model is based on behavior to win over others by strengthening social relationships with cooperators. The results of evolutionary simulations show the four classes of evolutionary dynamics. The results depend on total resources and the ratio of each cooperator's resource to the number of cooperators. One of the four classes is similar to a human strategy, i.e. the strategies based on the Yule--Simon process of power law.Comment: 21 pages, 10 figure

Understanding informal institutions: Networks and communities in rural development

A major theme within the literature on rural development is that the particular mix of formal and informal institutions present in any situation is a key determinant of development outcomes. However, there is some evidence that in policy and practice there are considerable difficulties in articulating formal organizational realities with the rules and norms embedded in informally constructed social structures. The same difficulty is in evidence in the New Institutional Economics, where the mainstream literature concedes the critical importance of informal and cultural institutions, but has thus far failed to develop an adequate theory of the informal. This recognized weakness is all the more urgent because of the growing emphasis on governance, participation and social learning evident in European rural development policy and practice. A clear understanding of the opportunities and pitfalls that arise in working with informal institutions is required, and therefore theories that provide analytical and operational traction in the 'parallel' realities of the formal and the informal. This paper starts from the point of view that at the heart of the institutional dilemma lies a difficulty in conceptualising the informal social structures in which informal institutions are reproduced. A review of relevant bodies of theory is presented; drawing on sociological network theory, perspectives on governance and social capital, and new developments in the organisational and management literature. These suggest some starting points for a theory of informal social realities and the institutions that structure them. The paper concludes with a presentation of a theoretical framework for understanding informal structures in rural development in terms of networks and communities