Evaluating balance on social networks from their simple cycles

Signed networks have long been used to represent social relations of amity (+) and enmity (-) between individuals. Group of individuals who are cyclically connected are said to be balanced if the number of negative edges in the cycle is even and unbalanced otherwise. In its earliest and most natural formulation, the balance of a social network was thus defined from its simple cycles, cycles which do not visit any vertex more than once. Because of the inherent difficulty associated with finding such cycles on very large networks, social balance has since then been studied via other means. In this article we present the balance as measured from the simple cycles and primitive orbits of social networks. We specifically provide two measures of balance: the proportion R` of negative simple cycles of length ` for each ` 6 20 which generalises the triangle index, and a ratio K` which extends the relative signed clustering coefficient introduced by Kunegis. To do so, we use a Monte Carlo implementation of a novel exact formula for counting the simple cycles on any weighted directed graph. Our method is free from the double-counting problem affecting previous cycle-based approaches, does not require edge-reciprocity of the underlying network, provides a gray-scale measure of balance for each cycle length separately and is sufficiently tractable that it can be implemented on a standard desktop computer. We observe that social networks exhibit strong inter-edge correlations favouring balanced situations and we determine the corresponding correlation length x . For longer simple cycles, R` undergoes a sharp transition to values expected from an uncorrelated model. This transition is absent from synthetic random networks, strongly suggesting that it carries a sociological meaning warranting further research

Evaluating balance on social networks from their simple cycles

Signed networks have long been used to represent social relations of amity (+) and enmity (-) between individuals. Group of individuals who are cyclically connected are said to be balanced if the number of negative edges in the cycle is even and unbalanced otherwise. In its earliest and most natural formulation, the balance of a social network was thus defined from its simple cycles, cycles which do not visit any vertex more than once. Because of the inherent difficulty associated with finding such cycles on very large networks, social balance has since then been studied via other means. In this article we present the balance as measured from the simple cycles and primitive orbits of social networks. We specifically provide two measures of balance: the proportion R` of negative simple cycles of length ` for each ` 6 20 which generalises the triangle index, and a ratio K` which extends the relative signed clustering coefficient introduced by Kunegis. To do so, we use a Monte Carlo implementation of a novel exact formula for counting the simple cycles on any weighted directed graph. Our method is free from the double-counting problem affecting previous cycle-based approaches, does not require edge-reciprocity of the underlying network, provides a gray-scale measure of balance for each cycle length separately and is sufficiently tractable that it can be implemented on a standard desktop computer. We observe that social networks exhibit strong inter-edge correlations favouring balanced situations and we determine the corresponding correlation length x . For longer simple cycles, R` undergoes a sharp transition to values expected from an uncorrelated model. This transition is absent from synthetic random networks, strongly suggesting that it carries a sociological meaning warranting further research

Evaluating case studies of community-oriented integrated care.

This paper summarises a ten-year conversation within London Journal of Primary Care about the nature of community-oriented integrated care (COIC) and how to develop and evaluate it. COIC means integration of efforts for combined disease-treatment and health-enhancement at local, community level. COIC is similar to the World Health Organisation concept of a Community-Based Coordinating Hub - both require a local geographic area where different organisations align their activities for whole system integration and develop local communities for health. COIC is a necessary part of an integrated system for health and care because it enables multiple insights into 'wicked problems', and multiple services to integrate their activities for people with complex conditions, at the same time helping everyone to collaborate for the health of the local population. The conversation concludes seven aspects of COIC that warrant further attention