Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of distributed computation. However, in many real networks nodes communicate efficiently even without such global intelligence. Here we show that the peculiar structural characteristics of many complex networks support efficient communication without global knowledge. We also describe a general mechanism that explains this connection between network structure and function. This mechanism relies on the presence of a metric space hidden behind an observable network. Our findings suggest that real networks in nature have underlying metric spaces that remain undiscovered. Their discovery would have practical applications ranging from routing in the Internet and searching social networks, to studying information flows in neural, gene regulatory networks, or signaling pathways.
Deep Dive into Navigability of Complex Networks.
Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of distributed computation. However, in many real networks nodes communicate efficiently even without such global intelligence. Here we show that the peculiar structural characteristics of many complex networks support efficient communication without global knowledge. We also describe a general mechanism that explains this connection between network structure and function. This mechanism relies on the presence of a metric space hidden behind an observable network. Our findings suggest that real networks in nature have underlying metric spaces that remain undiscovered. Their discovery would have practical applications ranging from routing in the Internet and searching social networks, to studying information flows in neural, gene regulatory networks, or signal
Networks are ubiquitous in all domains of science and technology, and permeate many aspects of daily human life [1,2,3,4], especially upon the rise of the information technology society [5,6]. Our growing dependence on them has inspired a burst of activity in the new field of network science, keeping researchers motivated to solve the difficult challenges that networks offer. Among these, the relation between network structure and function is perhaps the most important and fundamental. Transport is one of the most common functions of networked systems. Examples can be found in many domains: transport of energy in metabolic networks, of mass in food webs, of people in transportation systems, of information in cell signalling processes, or of bytes across the Internet.
In many of these examples, routing -or signalling of information propagation paths through a complex network maze-plays a determinant role in the transport properties of the system, in particular in such systems as the Internet or airport networks that have transport as their primary function. The observed efficiency of this routing process in real networks poses an intriguing question: how is this efficiency achieved? When each element of the system has a full view of the global network topology, finding short routes to target destinations is a well-understood computational process. However, in many networks observed in nature, including those in society and biology (signalling pathways, neural networks, etc.), nodes efficiently find intended communication targets even though they do not possess any global view of the system. For example, neural networks would not function so well if they could not route specific signals to appropriate organs or muscles in the body, although no neurone has a full view of global inter-neurone connectivity in the brain.
In this work, we identify a general mechanism that explains routing conductivity, or navigability of real networks based on the concept of similarity between nodes [7,8,9,10,11,12]. Specifically, intrinsic characteristics of nodes define a measure of similarity between them, which we abstract as a hidden distance. Taken together, hidden distances define a hidden metric space for a given network. Our recent work shows that these spaces explain the observed structural peculiarities of several real networks, in particular social and technological ones [13]. Here we show that this underlying metric structure can be used to guide the routing process, leading to efficient communication without global information in arbitrarily large networks. Our analysis reveals that, remarkably, real networks satisfy the topological conditions that maximise their navigability within this framework. Therefore, hidden metric spaces offer explanations of two open problems in complex networks science: the communication efficiency networks so often exhibit, and their unique structural characteristics.
Our work is inspired by the seminal work of sociologist Stanley Milgram on the small world problem. The small world paradigm refers to the existence of short chains of acquaintances among individuals in societies [14]. At Milgram’s time, direct proof of such a paradigm was impossible due to the lack of large databases of social contacts, so Milgram conceived an experiment to analyse the small world phenomenon in human social networks. Randomly chosen individuals in the United States were asked to route a letter to an unknown recipient using only friends or acquaintances that, according to their judgement, seemed most likely to know the intended recipient. The outcome of the experiment revealed that, without any global network knowledge, letters reached the target recipient using, on average, 5.2 intermediate people, demonstrating that social acquaintance networks were indeed small worlds.
The small world property can be easily induced by adding a small number of random connections to a “large world” network [15]. More striking is the fact that social networks are navigable without global information. Indeed, the only information that people used to make their routing decisions in Milgram’s experiment was a set of descriptive attributes of the destined recipient, such as place of living and occupation. People then determined who among their contacts was “socially closest” to the target. The success of the experiment indicates that social distances among individuals -even though they may be difficult to define mathematically-play a role in shaping the network architecture and that, at the same time, these distances can be used to navigate the network. However, it is not clear how this coupling between the structure and function of the network leads to efficiency of the search process, or what the minimum structural requirements are to facilitate such efficiency [16].
In this work, we show how network navigability depends on the structural parameters characterising the two most prominent and common properties of real compl
…(Full text truncated)…
This content is AI-processed based on ArXiv data.
