Growing local likelihood network: Emergence of communities

In many real situations, networks grow only via local interactions. New nodes are added to the growing network with only information pertaining to a small subset of existing nodes. Multilevel marketing, social networks, and diseases models can all be depicted as growing networks based on local distance information. In these examples, all nodes whose distance from a chosen center is less than d form a subgraph. We thence grow networks with information only from these subgraphs. Moreover, we use a likelihood-based method, where at each step we modify the networks in the way that will make the graph closer to the expected degree distribution. Combining local information and the likelihood method, we grow networks that exhibit novel features. We discover that the likelihood method, at certain parameter ranges, can generate networks with highly modulated communities, even when global information is not available. Communities and clusters are abundant in real-life networks, and the method proposed here provides a natural mechanism for the emergence of communities in scale-free networks. In addition, the algorithmic implementation of network growth via local information is substantially faster than global methods and allows for the exploration of much larger networks. Introduction. – Many systems in the physical and 1 biological realms exhibit behaviours governed by local 2 rather than global interaction. Growth of such systems 3 is often governed by local knowledge — when a new 4 node is added to the network, it is not provided with 5 perfect global information. Examples abound in different 6 fields [1, 2]. Social relationship, computers under virus 7 attack, and insects affected by infectious diseases all form 8 networks based on local evolving rules. 9