Dynamical properties of model communication networks

We study the dynamical properties of a collection of models for communication processes, characterized by a single parameter $\xi$ representing the relation between information load of the nodes and its ability to deliver this information. The critical transition to congestion reported so far occurs only for $\xi=1$. This case is well analyzed for different network topologies. We focus of the properties of the order parameter, the susceptibility and the time correlations when approaching the critical point. For $\xi<1$ no transition to congestion is observed but it remains a cross-over from a low-density to a high-density state. For $\xi>1$ the transition to congestion is discontinuous and congestion nuclei arise.Comment: 8 pages, 8 figure

Classes of complex networks defined by role-to-role connectivity profiles

Interactions between units in phyical, biological, technological, and social systems usually give rise to intrincate networks with non-trivial structure, which critically affects the dynamics and properties of the system. The focus of most current research on complex networks is on global network properties. A caveat of this approach is that the relevance of global properties hinges on the premise that networks are homogeneous, whereas most real-world networks have a markedly modular structure. Here, we report that networks with different functions, including the Internet, metabolic, air transportation, and protein interaction networks, have distinct patterns of connections among nodes with different roles, and that, as a consequence, complex networks can be classified into two distinct functional classes based on their link type frequency. Importantly, we demonstrate that the above structural features cannot be captured by means of often studied global properties

Detecting rich-club ordering in complex networks

Uncovering the hidden regularities and organizational principles of networks arising in physical systems ranging from the molecular level to the scale of large communication infrastructures is the key issue for the understanding of their fabric and dynamical properties [1-5]. The ``rich-club'' phenomenon refers to the tendency of nodes with high centrality, the dominant elements of the system, to form tightly interconnected communities and it is one of the crucial properties accounting for the formation of dominant communities in both computer and social sciences [4-8]. Here we provide the analytical expression and the correct null models which allow for a quantitative discussion of the rich-club phenomenon. The presented analysis enables the measurement of the rich-club ordering and its relation with the function and dynamics of networks in examples drawn from the biological, social and technological domains.Comment: 1 table, 3 figure

Extracting the hierarchical organization of complex systems

Extracting understanding from the growing ``sea'' of biological and socio-economic data is one of the most pressing scientific challenges facing us. Here, we introduce and validate an unsupervised method that is able to accurately extract the hierarchical organization of complex biological, social, and technological networks. We define an ensemble of hierarchically nested random graphs, which we use to validate the method. We then apply our method to real-world networks, including the air-transportation network, an electronic circuit, an email exchange network, and metabolic networks. We find that our method enables us to obtain an accurate multi-scale descriptions of a complex system.Comment: Figures in screen resolution. Version with full resolution figures available at http://amaral.chem-eng.northwestern.edu/Publications/Papers/sales-pardo-2007.pd

Theoretical approach and impact of correlations on the critical packet generation rate in traffic dynamics on complex networks

Using the formalism of the biased random walk in random uncorrelated networks with arbitrary degree distributions, we develop theoretical approach to the critical packet generation rate in traffic based on routing strategy with local information. We explain microscopic origins of the transition from the flow to the jammed phase and discuss how the node neighbourhood topology affects the transport capacity in uncorrelated and correlated networks.Comment: 6 pages, 5 figure

Mesoscopic organization reveals the constraints governing C. elegans nervous system

One of the biggest challenges in biology is to understand how activity at the cellular level of neurons, as a result of their mutual interactions, leads to the observed behavior of an organism responding to a variety of environmental stimuli. Investigating the intermediate or mesoscopic level of organization in the nervous system is a vital step towards understanding how the integration of micro-level dynamics results in macro-level functioning. In this paper, we have considered the somatic nervous system of the nematode Caenorhabditis elegans, for which the entire neuronal connectivity diagram is known. We focus on the organization of the system into modules, i.e., neuronal groups having relatively higher connection density compared to that of the overall network. We show that this mesoscopic feature cannot be explained exclusively in terms of considerations, such as optimizing for resource constraints (viz., total wiring cost) and communication efficiency (i.e., network path length). Comparison with other complex networks designed for efficient transport (of signals or resources) implies that neuronal networks form a distinct class. This suggests that the principal function of the network, viz., processing of sensory information resulting in appropriate motor response, may be playing a vital role in determining the connection topology. Using modular spectral analysis, we make explicit the intimate relation between function and structure in the nervous system. This is further brought out by identifying functionally critical neurons purely on the basis of patterns of intra- and inter-modular connections. Our study reveals how the design of the nervous system reflects several constraints, including its key functional role as a processor of information.Comment: Published version, Minor modifications, 16 pages, 9 figure

eBay users form stable groups of common interest

Market segmentation of an online auction site is studied by analyzing the users' bidding behavior. The distribution of user activity is investigated and a network of bidders connected by common interest in individual articles is constructed. The network's cluster structure corresponds to the main user groups according to common interest, exhibiting hierarchy and overlap. Key feature of the analysis is its independence of any similarity measure between the articles offered on eBay, as such a measure would only introduce bias in the analysis. Results are compared to null models based on random networks and clusters are validated and interpreted using the taxonomic classifications of eBay categories. We find clear-cut and coherent interest profiles for the bidders in each cluster. The interest profiles of bidder groups are compared to the classification of articles actually bought by these users during the time span 6-9 months after the initial grouping. The interest profiles discovered remain stable, indicating typical interest profiles in society. Our results show how network theory can be applied successfully to problems of market segmentation and sociological milieu studies with sparse, high dimensional data.Comment: Major revision of the manuscript. Methodological improvements and inclusion of analysis of temporal development of user interests. 19 pages, 12 figures, 5 table

Second-Order Assortative Mixing in Social Networks

In a social network, the number of links of a node, or node degree, is often assumed as a proxy for the node's importance or prominence within the network. It is known that social networks exhibit the (first-order) assortative mixing, i.e. if two nodes are connected, they tend to have similar node degrees, suggesting that people tend to mix with those of comparable prominence. In this paper, we report the second-order assortative mixing in social networks. If two nodes are connected, we measure the degree correlation between their most prominent neighbours, rather than between the two nodes themselves. We observe very strong second-order assortative mixing in social networks, often significantly stronger than the first-order assortative mixing. This suggests that if two people interact in a social network, then the importance of the most prominent person each knows is very likely to be the same. This is also true if we measure the average prominence of neighbours of the two people. This property is weaker or negative in non-social networks. We investigate a number of possible explanations for this property. However, none of them was found to provide an adequate explanation. We therefore conclude that second-order assortative mixing is a new property of social networks.Comment: Cite as: Zhou S., Cox I.J., Hansen L.K. (2017) Second-Order Assortative Mixing in Social Networks. In: Goncalves B., Menezes R., Sinatra R., Zlatic V. (eds) Complex Networks VIII. CompleNet 2017. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-54241-6_

The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles

We analyze the global structure of the world-wide air transportation network, a critical infrastructure with an enormous impact on local, national, and international economies. We find that the world-wide air transportation network is a scale-free small-world network. In contrast to the prediction of scale-free network models, however, we find that the most connected cities are not necessarily the most central, resulting in anomalous values of the centrality. We demonstrate that these anomalies arise because of the multi-community structure of the network. We identify the communities in the air transportation network and show that the community structure cannot be explained solely based on geographical constraints, and that geo-political considerations have to be taken into account. We identify each city's global role based on its pattern of inter- and intra-community connections, which enables us to obtain scale-specific representations of the network.Comment: Revised versio