Lucas Antiqueira

Analyzing and modeling real-world phenomena with complex networks: a survey of applications

The success of new scientific areas can be assessed by their potential in contributing to new theoretical approaches and in applications to real-world problems. Complex networks have fared extremely well in both of these aspects, with their sound theoretical basis being developed over the years and with a variety of applications. In this survey, we analyze the applications of complex networks to real-world problems and data, with emphasis in representation, analysis and modeling. A diversity of phenomena are surveyed, which may be classified into no less than 11 areas, providing a clear indication of the impact of the field of complex networks.

A complex network approach to text summarization

Automatic summarization of texts is now crucial for several information retrieval tasks owing to the huge amount of information available in digital media, which has increased the demand for simple, language-independent extractive summarization strategies. In this paper, we employ concepts and metrics of complex networks to select sentences for an extractive summary. The graph or network representing one piece of text consists of nodes corresponding to sentences, while edges connect sentences that share common meaningful nouns. Because various metrics could be used, we developed a set of 14 summarizers, generically referred to as CN-Summ, employing network concepts such as node degree, length of shortest paths, d-rings and k-cores. An additional summarizer was created which selects the highest ranked sentences in the 14 systems, as in a voting system. When applied to a corpus of Brazilian Portuguese texts, some CN-Summ versions performed better than summarizers that do not employ deep linguistic knowledge, with results comparable to state-of-the-art summarizers based on expensive linguistic resources. The use of complex networks to represent texts appears therefore as suitable for automatic summarization, consistent with the belief that the metrics of such networks may capture important text features.

COMPLEX NETWORKS ANALYSIS OF MANUAL AND MACHINE TRANSLATIONS

Complex networks have been increasingly used in text analysis, including in connection with natural language processing tools, as important text features appear to be captured by the topology and dynamics of the networks. Following previous works that apply complex networks concepts to text quality measurement, summary evaluation, and author characterization, we now focus on machine translation (MT). In this paper we assess the possible representation of texts as complex networks to evaluate cross-linguistic issues inherent in manual and machine translation. We show that different quality translations generated by MT tools can be distinguished from their manual counterparts by means of metrics such as in- (ID) and out-degrees (OD), clustering coefficient (CC), and shortest paths (SP). For instance, we demonstrate that the average OD in networks of automatic translations consistently exceeds the values obtained for manual ones, and that the CC values of source texts are not preserved for manual translations, but are for good automatic translations. This probably reflects the text rearrangements humans perform during manual translation. We envisage that such findings could lead to better MT tools and automatic evaluation metrics.

Correlations between structure and random walk dynamics in directed complex networks

In this letter the authors discuss the relationship between structure and random walk dynamics in directed complex networks, with an emphasis on identifying whether a topological hub is also a dynamical hub. They establish the necessary conditions for networks to be topologically and dynamically fully correlated (e.g., word adjacency and airport networks), and show that in this case Zipf’s law is a consequence of the match between structure and dynamics. They also show that real-world neuronal networks and the world wide web are not fully correlated, implying that their more intensely connected nodes are not necessarily highly active.

Modeling and evaluating summaries using complex networks

This paper presents a summary evaluation method based on a complex network measure. We show how to model summaries as complex networks and establish a possible correlation between summary quality and the measure known as dynamics of the network growth. It is a generic and language independent method that enables easy and fast comparative evaluation of summaries. We evaluate our approach using manually produced summaries and automatic summaries produced by three automatic text summarizers for the Brazilian Portuguese language. The results are in agreement with human intuition and showed to be statistically significant.

Characterization of subgraph relationships and distribution in complex networks

A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel approach which extends from single nodes to the whole network level by considering non-overlapping subgraphs (i.e. connected components) and their interrelationships and distribution through the network. Though such subgraphs can be completely general, our methodology focuses on the cases in which the nodes of these subgraphs share some special feature, such as being critical for the proper operation of the network. The methodology of subgraph characterization involves two main aspects: (i) the generation of histograms of subgraph sizes and distances between subgraphs and (ii) a merging algorithm, developed to assess the relevance of nodes outside subgraphs by progressively merging subgraphs until the whole network is covered. The latter procedure complements the histograms by taking into account the nodes lying between subgraphs, as well as the relevance of these nodes to the overall subgraph interconnectivity. Experiments were carried out using four types of network models and five instances of real-world networks, in order to illustrate how subgraph characterization can help complementing complex network-based studies.

Modeling connectivity in terms of network activity

A new complex network model is proposed which is founded on growth, with new connections being established proportionally to the current dynamical activity of each node, which can be understood as a generalization of the Barabasi–Albert static model. By using several topological measurements, as well as optimal multivariate methods (canonical analysis and maximum likelihood decision), we show that this new model provides, among several other theoretical kinds of networks including Watts–Strogatz small-world networks, the greatest compatibility with three real-world cortical networks.

Structure-Dynamics Interplay in Directed Complex Networks with Border Effects

Despite the large number of structural and dynamical properties investigated on complex networks, understanding their interrelationships is also of substantial importance to advance our knowledge on the organizing principles underlying such structures. We use a novel approach to study structure-dynamics correlations where the nodes of directed complex networks were partitioned into border and non-border by using the so-called diversity measurement. The network topology is characterized by the node degree, the most direct indicator of node connectivity, while the dynamics is related to the steady-state random walker occupation probability (called here node activity). Correlations between degree and activity were then analyzed inside and outside the border, separately. The obtained results showed that the intricate correlations found in the macaque cortex and in a WWW subgraph are in fact composed of two separate correlations of in-degree against the activity occurring inside and outside the border. These findings pave the way to investigations of possibly similar behavior in other directed complex networks.

Structural Relationships between Spiking Neural Networks and Functional Samples

Models of spiking neural networks have a great potential to become a crucial tool in the development of complex network theory. Of particular interest, these models can be used to better understand the important class of brain functional networks, which are frequently studied in the context of computational network analysis. A fundamental question is whether functional connectivity sampling via surface multichannel recordings is able to reproduce the main connectivity features of the underlying spatial neural network. In this work we address this problem through computational modeling using the integrate-and-fire spiking neuron model, which enabled us to relate neural connectivity and the respective mesoscopic dynamics. Functional samples were then compared to an idealized spatial neural network model in terms of established topological network measurements. Results show that some measurements (e.g., betweenness centrality) are able to fairly approximate functional and spatial networks. Therefore, under specific circumstances of sampling size and simulation approach, it is possible to say that functional networks are able to reproduce connectivity features of the underlying neural network.