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In the past few years, the storage and analysis of large-scale and fast evolving networks present a great challenge. Therefore, a number of different techniques have been proposed for sampling large networks. In general, network exploration techniques approximate the original networks more accurately than random node and link selection. Yet, link selection with additional subgraph induction step outperforms most other techniques. In this paper, we apply subgraph induction also to random walk and forest-fire sampling. We analyze different real-world networks and the changes of their properties introduced by sampling. We compare several sampling techniques based on the match between the original networks and their sampled variants. The results reveal that the techniques with subgraph induction underestimate the degree and clustering distribution, while overestimate average degree and density of the original networks. Techniques without subgraph induction step exhibit exactly the opposite behavior. Hence, the performance of the sampling techniques from random selection category compared to network exploration sampling does not differ significantly, while clear differences exist between the techniques with subgraph induction step and the ones without it.

Science is a social process with far-reaching impact on our modern society. In the recent years, for the first time we are able to scientifically study the science itself. This is enabled by massive amounts of data on scientific publications that is increasingly becoming available. The data is contained in several databases such as Web of Science or PubMed, maintained by various public and private entities. Unfortunately, these databases are not always consistent, which considerably hinders this study. Relying on the powerful framework of complex networks, we conduct a systematic analysis of the consistency among six major scientific databases. We found that identifying a single "best" database is far from easy. Nevertheless, our results indicate appreciable differences in mutual consistency of different databases, which we interpret as recipes for future bibliometric studies., Comment: 20 pages, 5 figures, 4 tables

The basic indicators of a researcher's productivity and impact are still the number of publications and their citation counts. These metrics are clear, straightforward, and easy to obtain. When a ranking of scholars is needed, for instance in grant, award, or promotion procedures, their use is the fastest and cheapest way of prioritizing some scientists over others. However, due to their nature, there is a danger of oversimplifying scientific achievements. Therefore, many other indicators have been proposed including the usage of the PageRank algorithm known for the ranking of webpages and its modifications suited to citation networks. Nevertheless, this recursive method is computationally expensive and even if it has the advantage of favouring prestige over popularity, its application should be well justified, particularly when compared to the standard citation counts. In this study, we analyze three large datasets of computer science papers in the categories of artificial intelligence, software engineering, and theory and methods and apply 12 different ranking methods to the citation networks of authors. We compare the resulting rankings with self-compiled lists of outstanding researchers selected as frequent editorial board members of prestigious journals in the field and conclude that there is no evidence of PageRank-based methods outperforming simple citation counts., Comment: 28 pages, 5 figures, 6 tables

Any network studied in the literature is inevitably just a sampled representative of its real-world analogue. Additionally, network sampling is lately often applied to large networks to allow for their faster and more efficient analysis. Nevertheless, the changes in network structure introduced by sampling are still far from understood. In this paper, we study the presence of characteristic groups of nodes in sampled social and information networks. We consider different network sampling techniques including random node and link selection, network exploration and expansion. We first observe that the structure of social networks reveals densely linked groups like communities, while the structure of information networks is better described by modules of structurally equivalent nodes. However, despite these notable differences, the structure of sampled networks exhibits stronger characterization by community-like groups than the original networks, irrespective of their type and consistently across various sampling techniques. Hence, rich community structure commonly observed in social and information networks is to some extent merely an artifact of sampling., Comment: 15 pages, 6 figures, 5 tables

Many real-world networks are large, complex and thus hard to understand, analyze or visualize. The data about networks is not always complete, their structure may be hidden or they change quickly over time. Therefore, understanding how incomplete system differs from complete one is crucial. In this paper, we study the changes in networks under simplification (i.e., reduction in size). We simplify 30 real-world networks with six simplification methods and analyze the similarity between original and simplified networks based on preservation of several properties, for example degree distribution, clustering coefficient, betweenness centrality, density and degree mixing. We propose an approach for assessing the effectiveness of simplification process to define the most appropriate size of simplified networks and to determine the method, which preserves the most properties of original networks. The results reveal the type and size of original networks do not influence the changes of networks under simplification process, while the size of simplified networks does. Moreover, we investigate the performance of simplification methods when the size of simplified networks is 10% of the original networks. The findings show that sampling methods outperform merging ones, particularly random node selection based on degree and breadth-first sampling perform the best.

Large software projects are among most sophisticated human-made systems consisting of a network of interdependent parts. Past studies of software systems from the perspective of complex networks have already led to notable discoveries with different applications. Nevertheless, our comprehension of the structure of software networks remains to be only partial. We here investigate correlations or mixing between linked nodes and show that software networks reveal dichotomous node degree mixing similar to that recently observed in biological networks. We further show that software networks also reveal characteristic clustering profiles and mixing. Hence, node mixing in software networks significantly differs from that in, e.g., the Internet or social networks. We explain the observed mixing through the presence of groups of nodes with common linking pattern. More precisely, besides densely linked groups known as communities, software networks also consist of disconnected groups denoted modules, core/periphery structures and other. Moreover, groups coincide with the intrinsic properties of the underlying software projects, which promotes practical applications in software engineering., Comment: 26 pages, 14 figures, 11 tables

Modern bibliographic databases provide the basis for scientific research and its evaluation. While their content and structure differ substantially, there exist only informal notions on their reliability. Here we compare the topological consistency of citation networks extracted from six popular bibliographic databases including Web of Science, CiteSeer and arXiv.org. The networks are assessed through a rich set of local and global graph statistics. We first reveal statistically significant inconsistencies between some of the databases with respect to individual statistics. For example, the introduced field bow-tie decomposition of DBLP Computer Science Bibliography substantially differs from the rest due to the coverage of the database, while the citation information within arXiv.org is the most exhaustive. Finally, we compare the databases over multiple graph statistics using the critical difference diagram. The citation topology of DBLP Computer Science Bibliography is the least consistent with the rest, while, not surprisingly, Web of Science is significantly more reliable from the perspective of consistency. This work can serve either as a reference for scholars in bibliometrics and scientometrics or a scientific evaluation guideline for governments and research agencies., Comment: 16 pages, 3 figures, 3 tables

Complex real-world networks commonly reveal characteristic groups of nodes like communities and modules. These are of value in various applications, especially in the case of large social and information networks. However, while numerous community detection techniques have been presented in the literature, approaches for other groups of nodes are relatively rare and often limited in some way. We present a simple propagation-based algorithm for general group detection that requires no a priori knowledge and has near ideal complexity. The main novelty here is that different types of groups are revealed through an adequate hierarchical group refinement procedure. The proposed algorithm is validated on various synthetic and real-world networks, and rigorously compared against twelve other state-of-the-art approaches on group detection, hierarchy discovery and link prediction tasks. The algorithm is comparable to the state of the art in community detection, while superior in general group detection and link prediction. Based on the comparison, we also dis- cuss some prominent directions for future work on group detection in complex networks., Comment: 15 pages, 6 figures, 6 tables

Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by degree, which are also the properties captured by different random graph models proposed in the literature. However, many (non-social) real-world networks are in fact disassortative by degree. Thus, we here propose a simple evolving model that generates networks with most common properties of real-world networks including degree disassortativity. Furthermore, the model has a natural interpretation for citation networks with different practical applications.

Complex software systems are among most sophisticated human-made systems, yet only little is known about the actual structure of 'good' software. We here study different software systems developed in Java from the perspective of network science. The study reveals that network theory can provide a prominent set of techniques for the exploratory analysis of large complex software system. We further identify several applications in software engineering, and propose different network-based quality indicators that address software design, efficiency, reusability, vulnerability, controllability and other. We also highlight various interesting findings, e.g., software systems are highly vulnerable to processes like bug propagation, however, they are not easily controllable.

Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. Clustering, community structure and assortative mixing by degree are perhaps among most prominent examples of the latter. Although generally accepted for social networks, these properties only partially explain the structure of other networks. We first show that degree-corrected clustering is in contrast to standard definition highly assortative. Yet interesting on its own, we further note that non-social networks contain connected regions with very low clustering. Hence, the structure of real-world networks is beyond communities. We here investigate the concept of functional modules---groups of regularly equivalent nodes---and show that such structures could explain for the properties observed in non-social networks. Real-world networks might be composed of functional modules that are overlaid by communities. We support the latter by proposing a simple network model that generates scale-free small-world networks with tunable clustering and degree mixing. Model has a natural interpretation in many real-world networks, while it also gives insights into an adequate community extraction framework. We also present an algorithm for detection of arbitrary structural modules without any prior knowledge. Algorithm is shown to be superior to state-of-the-art, while application to real-world networks reveals well supported composites of different structural modules that are consistent with the underlying systems. Clear functional modules are identified in all types of networks including social. Our findings thus expose functional modules as another key ingredient of complex real-world networks., Comment: 21 pages, 15 figures, 7 tables

Despite their diverse origin, networks of large real-world systems reveal a number of common properties including small-world phenomena, scale-free degree distributions and modularity. Recently, network self-similarity as a natural outcome of the evolution of real-world systems has also attracted much attention within the physics literature. Here we investigate the scaling of density in complex networks under two classical box-covering renormalizations-network coarse-graining-and also different community-based renormalizations. The analysis on over 50 real-world networks reveals a power-law scaling of network density and size under adequate renormalization technique, yet irrespective of network type and origin. The results thus advance a recent discovery of a universal scaling of density among different real-world networks [Laurienti et al., Physica A 390 (20) (2011) 3608-3613.] and imply an existence of a scale-free density also within-among different self-similar scales of-complex real-world networks. The latter further improves the comprehension of self-similar structure in large real-world networks with several possible applications.

Community structure is largely regarded as an intrinsic property of complex real-world networks. However, recent studies reveal that networks comprise even more sophisticated modules than classical cohesive communities. More precisely, real-world networks can also be naturally partitioned according to common patterns of connections between the nodes. Recently, a propagation based algorithm has been proposed for the detection of arbitrary network modules. We here advance the latter with a more adequate community modeling based on network clustering. The resulting algorithm is evaluated on various synthetic benchmark networks and random graphs. It is shown to be comparable to current state-of-the-art algorithms, however, in contrast to other approaches, it does not require some prior knowledge of the true community structure. To demonstrate its generality, we further employ the proposed algorithm for community detection in different unipartite and bipartite real-world networks, for generalized community detection and also predictive data clustering.

Label propagation has proven to be an extremely fast method for detecting communities in large complex networks. Furthermore, due to its simplicity, it is also currently one of the most commonly adopted algorithms in the literature. Despite various subsequent advances, an important issue of the algorithm has not yet been properly addressed. Random (node) update orders within the algorithm severely hamper its robustness, and consequently also the stability of the identified community structure. We note that an update order can be seen as increasing propagation preferences from certain nodes, and propose a balanced propagation that counteracts for the introduced randomness by utilizing node balancers. We have evaluated the proposed approach on synthetic networks with planted partition, and on several real-world networks with community structure. The results confirm that balanced propagation is significantly more robust than label propagation, when the performance of community detection is even improved. Thus, balanced propagation retains high scalability and algorithmic simplicity of label propagation, but improves on its stability and performance.

Due to notable discoveries in the fast evolving field of complex networks, recent research in software engineering has also focused on representing software systems with networks. Previous work has observed that these networks follow scale-free degree distributions and reveal small-world phenomena, while we here explore another property commonly found in different complex networks, i.e. community structure. We adopt class dependency networks, where nodes represent software classes and edges represent dependencies among them, and show that these networks reveal a significant community structure, characterized by similar properties as observed in other complex networks. However, although intuitive and anticipated by different phenomena, identified communities do not exactly correspond to software packages. We empirically confirm our observations on several networks constructed from Java and various third party libraries, and propose different applications of community detection to software engineering.

The article proposes an expert system for detection, and subsequent investigation, of groups of collaborating automobile insurance fraudsters. The system is described and examined in great detail, several technical difficulties in detecting fraud are also considered, for it to be applicable in practice. Opposed to many other approaches, the system uses networks for representation of data. Networks are the most natural representation of such a relational domain, allowing formulation and analysis of complex relations between entities. Fraudulent entities are found by employing a novel assessment algorithm, \textit{Iterative Assessment Algorithm} (\textit{IAA}), also presented in the article. Besides intrinsic attributes of entities, the algorithm explores also the relations between entities. The prototype was evaluated and rigorously analyzed on real world data. Results show that automobile insurance fraud can be efficiently detected with the proposed system and that appropriate data representation is vital.

Community structure appears to be an intrinsic property of many complex real-world networks. However, recent work shows that real-world networks reveal even more sophisticated modules than classical cohesive (link-density) communities. In particular, networks can also be naturally partitioned according to similar patterns of connectedness among the nodes, revealing link-pattern communities. We here propose a propagation based algorithm that can extract both link-density and link-pattern communities, without any prior knowledge of the true structure. The algorithm was first validated on different classes of synthetic benchmark networks with community structure, and also on random networks. We have further applied the algorithm to different social, information, technological and biological networks, where it indeed reveals meaningful (composites of) link-density and link-pattern communities. The results thus seem to imply that, similarly as link-density counterparts, link-pattern communities appear ubiquitous in nature and design.

Label propagation has proven to be a fast method for detecting communities in large complex networks. Recent developments have also improved the accuracy of the approach, however, a general algorithm is still an open issue. We present an advanced label propagation algorithm that combines two unique strategies of community formation, namely, defensive preservation and offensive expansion of communities. Two strategies are combined in a hierarchical manner, to recursively extract the core of the network, and to identify whisker communities. The algorithm was evaluated on two classes of benchmark networks with planted partition and on almost 25 real-world networks ranging from networks with tens of nodes to networks with several tens of millions of edges. It is shown to be comparable to the current state-of-the-art community detection algorithms and superior to all previous label propagation algorithms, with comparable time complexity. In particular, analysis on real-world networks has proven that the algorithm has almost linear complexity, $\mathcal{O}(m^{1.19})$, and scales even better than basic label propagation algorithm ($m$ is the number of edges in the network).

Label propagation has proven to be a fast method for detecting communities in complex networks. Recent work has also improved the accuracy and stability of the basic algorithm, however, a general approach is still an open issue. We propose different label propagation algorithms that convey two unique strategies of community formation, namely, defensive preservation and offensive expansion of communities. Furthermore, the strategies are combined in an advanced label propagation algorithm that retains the advantages of both approaches; and are enhanced with hierarchical community extraction, prominent for the use on larger networks. The proposed algorithms were empirically evaluated on different benchmarks networks with planted partition and on over 30 real-world networks of various types and sizes. The results confirm the adequacy of the propositions and give promising grounds for future analysis of (large) complex networks. Nevertheless, the main contribution of this work is in showing that different types of networks (with different topological properties) favor different strategies of community formation.