Homophyly/Kinship Model: Naturally Evolving Networks

Abstract

It has been a challenge to understand the formation and roles of social groups or natural communities in the evolution of species, societies and real world networks. Here, we propose the hypothesis that homophyly/kinship is the intrinsic mechanism of natural communities, introduce the notion of the affinity exponent and propose the homophyly/kinship model of networks. We demonstrate that the networks of our model satisfy a number of topological, probabilistic and combinatorial properties and, in particular, that the robustness and stability of natural communities increase as the affinity exponent increases and that the reciprocity of the networks in our model decreases as the affinity exponent increases. We show that both homophyly/kinship and reciprocity are essential to the emergence of cooperation in evolutionary games and that the homophyly/kinship and reciprocity determined by the appropriate affinity exponent guarantee the emergence of cooperation in evolutionary games, verifying Darwin’s proposal that kinship and reciprocity are the means of individual fitness. We propose the new principle of structure entropy minimisation for detecting natural communities of networks and verify the functional module property and characteristic properties by a healthy tissue cell network, a citation network, some metabolic networks and a protein interaction network.

Structural Information and Dynamical Complexity of Networks

“…This is the reason why there is always an outside condition governing the algorithms of modularity maximisation. Our experiments in [31], [32], and [36] also showed that in most cases, the algorithms of modularity maximisation fail to detect natural communities (or ground-truth communities) of real world networks.…”

“…and b) creates d edges from v to nodes of the same colour in G i−1 , chosen with a probability proportional to the degrees in G i−1 . It has been shown [31] that the networks generated by the homophyly/kinship model truthfully reflects many real networks, including both biological networks and social networks. We have also demonstrated that the homophyly/kinship model provides a methodology for community analyses of networks [31].…”

“…The experiments in [31], [32], and [36] have shown that for both K = 2 and 3, K -dimensional structural information minimisation is in deed the currently best strategy to detect the natural structure, that is, the ground-truth structures of real world networks.…”

“…Theorem 27 indicates that if the conductance (G) of network G is large then the two-dimensional structural information H 2 (G) of G cannot be small. The challenge must be resolved by new theory of networks, consisting of both a local theory and a global theory such that the minimisation of two-dimensional structural information is realised by the local theory, and the expanding requirement is satisfied by a global core of the network that is an expander, details are referred to [31] and [34].…”

“…To understand the intrinsic mechanism of the natural communities of the networks that are naturally evolving, the authors and colleagues [31] proposed the homophyly/kinship model of networks to realise the networks naturally evolving in the real world. The model is established by paralleling the Darwin's evolution theory [18].…”