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Most existing works on transportation dynamics focus on networks of a fixed structure, but networks whose nodes are mobile have become widespread, such as cell-phone networks. We introduce a model to explore the basic physics of transportation on mobile networks. Of particular interest are the dependence of the throughput on the speed of agent movement and communication range. Our computations reveal a hierarchical dependence for the former while, for the latter, we find an algebraic power law between the throughput and the communication range with an exponent determined by the speed. We develop a physical theory based on the Fokker-Planck equation to explain these phenomena. Our findings provide insights into complex transportation dynamics arising commonly in natural and engineering systems.
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We present a novel model to simulate real social networks of complex interactions, based in a granular system of colliding particles (agents). The network is build by keeping track of the collisions and evolves in time with correlations which emerge due to the mobility of the agents. Therefore, statistical features are a consequence only of local collisions among its individual agents. Agent dynamics is realized by an event-driven algorithm of collisions where energy is gained as opposed to granular systems which have dissipation. The model reproduces empirical data from networks of sexual interactions, not previously obtained with other approaches.
Modern world builds on the resilience of interdependent infrastructures characterized as complex networks. Recently, a framework for analysis of interdependent networks has been developed to explain the mechanism of resilience in interdependent networks. Here we extend this interdependent network model by considering flows in the networks and study the systems resilience under different attack strategies. In our model, nodes may fail due to either overload or loss of interdependency. Under the interaction between these two failure mechanisms, it is shown that interdependent scale-free networks show extreme vulnerability. The resilience of interdependent SF networks is found in our simulation much smaller than single SF network or interdependent SF networks without flows.
Multimodal transportation systems can be represented as time-resolved multilayer networks where different transportation modes connecting the same set of nodes are associated to distinct network layers. Their quantitative description became possible recently due to openly accessible datasets describing the geolocalised transportation dynamics of large urban areas. Advancements call for novel analytics, which combines earlier established methods and exploits the inherent complexity of the data. Here, our aim is to provide a novel user-based methodological framework to represent public transportation systems considering the total travel time, its variability across the schedule, and taking into account the number of transfers necessary. Using this framework we analyse public transportation systems in several French municipal areas. We incorporate travel routes and times over multiple transportation modes to identify efficient transportation connections and non-trivial connectivity patterns. The proposed method enables us to quantify the networks overall efficiency as compared to the specific demand and to the car alternative.
We propose a model of mobile agents to construct social networks, based on a system of moving particles by keeping track of the collisions during their permanence in the system. We reproduce not only the degree distribution, clustering coefficient and shortest path length of a large data base of empirical friendship networks recently collected, but also some features related with their community structure. The model is completely characterized by the collision rate and above a critical collision rate we find the emergence of a giant cluster in the universality class of two-dimensional percolation. Moreover, we propose possible schemes to reproduce other networks of particular social contacts, namely sexual contacts.
Pathways of diffusion observed in real-world systems often require stochastic processes going beyond first-order Markov models, as implicitly assumed in network theory. In this work, we focus on second-order Markov models, and derive an analytical expression for the effect of memory on the spectral gap and thus, equivalently, on the characteristic time needed for the stochastic process to asymptotically reach equilibrium. Perturbation analysis shows that standard first-order Markov models can either overestimate or underestimate the diffusion rate of flows across the modular structure of a system captured by a second-order Markov network. We test the theoretical predictions on a toy example and on numerical data, and discuss their implications for network theory, in particular in the case of temporal or multiplex networks.
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