Abstract. Modular structure is ubiquitous in real-world complex networks, and its detection is important because it gives insights in the structure-functionality relationship. The standard approach is based on the optimization of a quality function, modularity, which is a relative quality measure for a partition of a network into modules. Recently some authors [1, 2] have pointed out that the optimization of modularity has a fundamental drawback: the existence of a resolution limit beyond which no modular structure can be detected even though these modules might have own entity. The reason is that several topological descriptions of the network coexist at different scales, which is, in general, a fingerprint of complex systems. Here we propose a method that allows for multiple resolution screening of the modular structure. The method has been validated using synthetic networks, discovering the predefined structures at all scales. Its application to two real social networks allows to find the exact splits reported in the literature, as well as the substructure beyond the actual split. PACS number: 89.75

ubiquitous computing environments

In this paper, we introduce a method for analyzing the temporal dynamics of affiliation networks. We define affiliation groups which describe temporally related subsets of actors and describe an approach for exploring changing memberships in these affiliation groups over time. To model the dynamic behavior in these networks, we consider the concept of loyalty and introduce a measure that captures an actor’s loyalty to an affiliation group as the degree of ‘commitment ’ an actor shows to the group over time. We evaluate our measure using three real world affiliation networks: a publication network, a senate bill cosponsorship network and a dolphin network. The results show the utility of our measure for analyzing the dynamic behavior of actors and quantifying their loyalty to different time-varying affiliation groups. 1

The relationships among modules in a software project of a certain size can give us much information about its internal organization and a way to control and monitor development activities and evolution of large libre software projects. In this paper, we show how information available in CVS repositories can be used to study the structure of the modules in a project when they are related by the people working in them, and how techniques taken from the social networks fields can be used to highlight the characteristics of that structure. As a case example, we also show some results of applying this methodology to the Apache project in several points in time. Among other facts, it is shown how the project evolves and is self-structuring, with developer communities of modules corresponding to semantically related families of modules.

This paper presents a framework and methodology to improve the search experience in digital library systems. The approach taken is to cluster a textual knowledgebase along multiple relations and return search results in the form of small, focused clusters. Specifically, we generate multiple relationship networks, one per relationship type, and then cluster these networks. At search time, we present a ranked set of clusters—one ranking per relationship type. The intuition for this approach is that returning clusters of contextually related information provides users with a situational and contextual awareness of the search results rather than returning a ranked list of only those documents that match the query. We address the use of both implicit (such as textual content) and explicit (such as citations, authors etc.) relations between documents. The primary question we focus on is how to rank the clusters, given a search query. We explore two approaches: a text-based rank (using the text‘s similarity to the user‘s query) and a social network-based rank (using information centrality). A comparison of these two ranking methods suggest that using information centrality for ranking is very useful for ranking clusters and its documents because the documents that characterize that cluster get the highest rank. 1.

As online discussion boards become a popular medium for collaborative problem solving, we would like to understand patterns of group interactions that lead to collaborative learning and better performance. In this paper, we present an approach for assessing collaboration in online discussion, by profiling student-group participation. We use a modularity function to compute optimal discussion group partitions and then examine usage patterns with respect to high-versus lowparticipating students, and high- versus low-performing students as measured by grades. We apply the profiling technique to a discussion board of an undergraduate computer science course with three semesters of discussion data, comprising 142 users and 1620 messages. Several patterns are identified, and in particular, we show that high achievers tend to act as ‘bridges’, engaging in more diverse discussions with a wider group of peers.

multi-resolution community analysis

This paper presents a method for identifying a set of dense subgraphs of a given sparse graph. Within the main applications of this “dense subgraph problem”, the dense subgraphs are interpreted as communities, as in, e.g., social networks. The problem of identifying dense subgraphs helps analyze graph structures and complex networks and it is known to be challenging. It bears some similarities with the problem of reordering/blocking matrices in sparse matrix techniques. We exploit this link and adapt the idea of recognizing matrix column similarities, in order to compute a partial clustering of the vertices in a graph, where each cluster represents a dense subgraph. In contrast to existing subgraph extraction techniques which are based on a complete clustering of the graph nodes, the proposed algorithm takes into account the fact that not every participating node in the network needs to belong to a community. Another advantage is that the method does not require to specify the number of clusters; this number is usually not known in advance and is difficult to estimate. The computational process is very efficient, and the effectiveness of the proposed method is demonstrated in a few real-life examples.

A graph theoretic approach is proposed to formulate communication graphs that enable ultrafast information distribution. In our earlier work, we reported that Borel Cayley graph (BCG) is potentially a good candidate as a logical topology for fast information distribution. However, the practical applications of BCG have been challenging because of its inflexible sizes. In this paper, we propose a simple but effective graph resizing algorithm that removes nodes from an oversized BCG to achieve a desired network size. The proposed resizing algorithm consists of two parts: a random pruning algorithm that identifies nodes to be removed uniformly at random; and a novel Cut-Through Rewiring (CTR) algorithm that rewires the remaining nodes. The proposed resizing algorithm preserves the superior properties of the original BCGs, including a small diameter, a short average path length, a large algebraic connectivity, and ultrafast information distribution performance. Analytical formulae were also derived to compute the graph disconnection probability of the BCGs after resizing. Analytical results showed that the resized graphs were almost surely connected even after 80%∼90 % size reduction, depending on the original BCG size.

open–access journal for physics Fundamental statistical features and self-similar properties of tagged networks