Network theory

About: Network theory is a research topic. Over the lifetime, 2257 publications have been published within this topic receiving 109864 citations.

The Many Faces of Graph Dynamics

Abstract: The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is known today about the network dynamics: indeed, complex networks in reality are not static, but rather dynamically evolve over time. Our paper is motivated by the empirical observation that network evolution patterns seem far from random, but exhibit structure. Moreover, the specific patterns appear to depend on the network type, contradicting the existence of a "one fits it all" model. However, we still lack observables to quantify these intuitions, as well as metrics to compare graph evolutions. Such observables and metrics are needed for extrapolating or predicting evolutions, as well as for interpolating graph evolutions. To explore the many faces of graph dynamics and to quantify temporal changes, this paper suggests to build upon the concept of centrality, a measure of node importance in a network. In particular, we introduce the notion of centrality distance, a natural similarity measure for two graphs which depends on a given centrality, characterizing the graph type. Intuitively, centrality distances reflect the extent to which (non-anonymous) node roles are different or, in case of dynamic graphs, have changed over time, between two graphs. We evaluate the centrality distance approach for five evolutionary models and seven real-world social and physical networks. Our results empirically show the usefulness of centrality distances for characterizing graph dynamics compared to a null-model of random evolution, and highlight the differences between the considered scenarios. Interestingly, our approach allows us to compare the dynamics of very different networks, in terms of scale and evolution speed.

Efficient algorithm for ranking of nodes' importance in information dissemination

Abstract: Identifying nodes that play important roles in network dynamics in large scale complex networks is crucial for both characterizing the network and resource management. Under the viral marketing setting, Diffusion Centrality (DC) estimates the influential power of an individual. For the transport and physics communities, a node is considered important in Markov centrality (MC) if it can be quickly reached from the other nodes. Because these networks could contain millions of nodes, any ranking algorithm must have low time requirements to be practically useful. In this paper, we show that both metrics are strongly correlated, and we present a new method to enable fast estimation of the two metrics for large scale networks. The new approach is further validated empirically by using both real and synthetic networks. Our results refined the intuition that the influential power of an individual is largely governed by the local topology, rather than the mere number of contacts (node degree) alone. This allows us to better characterize the properties of the nodes that affect the outcome of the two centrality metrics.

Identifying clusters of complex urban-rural issues as part of policy making process using a network analysis approach: a case study in Bahía de Los Ángeles, Mexico.

Abstract: Improving human settlements diagnosis is a key factor in effective urban planning and the design of efficient policy making. In this paper, we illustrate how network theory concepts can be applied to reveal the topological structure of functional relationships in a network of heterogeneous urban–rural issues. This mapping is done using clustering algorithms and centrality value techniques. By analyzing emergent groups of urban–rural related issues, our methodology was applied to a rural community, considering in this exercise environmental matters and real estate interests as a way to better understand the structure of salient issues in the context of its urban development program design. Results show clusters that arrange themselves not by an obvious similarity in their constituent components, but by relations observed in urban–rural settings that hint on the issues that the urban development program must focus. Due to its complex nature, the classification of these emerging clusters and how they must be treated in traditional planning instruments is a new challenge that this novel methodology reveals.

Influence Study on Hyper-graphs

Abstract: Multilateral relations between entities lose their semantics when represented as simple graphs. Instead hypergraphs can naturally represent the said relations, which are common in social tagging systems. An important issue is the effect of the structural properties of a hypergraph on influence propagation. In the current work, an empirical study is undertaken to compare the effect of degree, k-shell and eigenvector centrality under the SIS, and SIR models of infection. The results on the MovieLens, Delicious and LastFM social networks indicate that k-shell centrality is a more accurate predictor of the influence of a node than degree centrality, and that eigenvector centrality is closely correlated with k-shell centrality.