A large body of work has been devoted to identifying community structure in networks. A community is often though of as a set of nodes that has more connections between its members than to the remainder of the network. In this paper, we characterize as a function of size the statistical and structural properties of such sets of nodes. We define the network community profile plot, which characterizes the “best ” possible community—according to the conductance measure—over a wide range of size scales, and we study over 70 large sparse real-world networks taken from a wide range of application domains. Our results suggest a significantly more refined picture of community structure in large real-world networks than has been appreciated previously. Our most striking finding is that in nearly every network dataset we examined, we observe tight but almost trivial communities at very small scales, and at larger size scales, the best possible communities gradually “blend in ” with the rest of the network and thus become less “community-like.” This behavior is not explained, even at a qualitative level, by any of the commonly-used network generation models. Moreover, this behavior is exactly the opposite of what one would expect based on experience with and intuition from expander graphs, from graphs that are well-embeddable in a low-dimensional structure, and from small social networks that have served as testbeds of community detection algorithms. We have found, however, that a generative model, in which new edges are added via an iterative “forest fire” burning process, is able to produce graphs exhibiting a network community structure similar to our observations.

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics and function of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements organized into classes. Special attention is given to relating complex network analysis with the areas of pattern recognition and feature selection, as well as on surveying some concepts and measurements from traditional graph theory which are potentially useful for complex network research. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the

Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advantages: it captures well the community structure in a network, it can be computed efficiently, and it can be used in an agglomerative algorithm to compute efficiently the community structure of a network. We propose such an algorithm, called Walktrap, which runs in time O(mn 2) and space O(n 2) in the worst case, and in time O(n 2 log n) and space O(n 2) in most real-world cases (n and m are respectively the number of vertices and edges in the input graph). Extensive comparison tests show that our algorithm surpasses previously proposed ones concerning the quality of the obtained community structures and that it stands among the best ones concerning the running time.

A large body of work has been devoted to defining and identifying clusters or communities in social and information networks, i.e., in graphs in which the nodes represent underlying social entities and the edges represent some sort of interaction between pairs of nodes. Most such research begins with the premise that a community or a cluster should be thought of as a set of nodes that has more and/or better connections between its members than to the remainder of the network. In this paper, we explore from a novel perspective several questions related to identifying meaningful communities in large social and information networks, and we come to several striking conclusions. Rather than defining a procedure to extract sets of nodes from a graph and then attempt to interpret these sets as a “real ” communities, we employ approximation algorithms for the graph partitioning problem to characterize as a function of size the statistical and structural properties of partitions of graphs that could plausibly be interpreted as communities. In particular, we define the network community profile plot, which characterizes the “best ” possible community—according to the conductance measure—over a wide range of size scales. We study over 100 large real-world networks, ranging from traditional and on-line social networks, to technological and information networks and

Community is an important attribute of Pocket Switched Networks (PSN), because mobile devices are carried by people who tend to belong to communities. We analysed community structure from mobility traces and used for forwarding algorithms [12], which shows significant impact of community. Here, we propose and evaluate three novel distributed community detection approaches with great potential to detect both static and temporal communities. We find that with suitable configuration of the threshold values, the distributed community detection can approximate their corresponding centralised methods up to 90 % accuracy.

The emergence of Delay Tolerant Networks (DTNs) has culminated in a new generation of wireless networking. We focus on a type of human-to-human communication in DTNs, where human behaviour exhibits the characteristics of networks by forming a community. We show the characteristics of such networks from extensive study of realworld human connectivity traces. We exploit distributed community detection from the trace and propose a Socio-Aware Overlay over detected communities for publish/subscribe communication. Centrality nodes have the best visibility to the other nodes in the network. We create an overlay with such centrality nodes from communities. Distributed community detection operates when nodes (i.e. devices) are in contact by gossipping, and subscription propagation is performed along with this operation. We validate our message dissemination algorithms for publish/subscribe with connectivity traces.

Detecting clusters or communities in large real-world graphs such as large social or information networks is a problem of considerable interest. In practice, one typically chooses an objective function that captures the intuition of a network cluster as set of nodes with better internal connectivity than external connectivity, and then one applies approximation algorithms or heuristics to extract sets of nodes that are related to the objective function and that “look like” good communities for the application of interest. In this paper, we explore a range of network community detection methods in order to compare them and to understand their relative performance and the systematic biases in the clusters they identify. We evaluate several common objective functions that are used to formalize the notion of a network community, and we examine several different classes of approximation algorithms that aim to optimize such objective functions. In addition, rather than simply fixing an objective and asking for an approximation to the best cluster of any size, we consider a size-resolved version of the optimization problem. Considering community quality as a function of its size provides a much finer lens with which to examine community detection algorithms, since objective functions and approximation algorithms often have non-obvious size-dependent behavior.

Recently, there has been much excitement in the research community over using social networks to mitigate multiple identity, or Sybil, attacks. A number of schemes have been proposed, but they differ greatly in the algorithms they use and in the networks upon which they are evaluated. As a result, the research community lacks a clear understanding of how these schemes compare against each other, how well they would work on real-world social networks with different structural properties, or whether there exist other (potentially better) ways of Sybil defense. In this paper, we show that, despite their considerable differences, existing Sybil defense schemes work by detecting local communities (i.e., clusters of nodes more tightly knit than the rest of the graph) around a trusted node. Our finding has important implications for both existing and future designs of Sybil defense schemes. First, we show that there is an opportunity to leverage the substantial amount of prior work on general community detection algorithms in order to defend against Sybils. Second, our analysis reveals the fundamental limits of current social network-based Sybil defenses: We demonstrate that networks with well-defined community structure are inherently more vulnerable to Sybil attacks, and that, in such networks, Sybils can carefully target their links in order make their attacks more effective.

Economic Forum within the framework of the

Online social networks are now a popular way for users to connect, express themselves, and share content. Users in today’s online social networks often post a profile, consisting of attributes like geographic location, interests, and schools attended. Such profile information is used on the sites as a basis for grouping users, for sharing content, and for suggesting users who may benefit from interaction. However, in practice, not all users provide these attributes. In this paper, we ask the question: given attributes for some fraction of the users in an online social network, can we infer the attributes of the remaining users? In other words, can the attributes of users, in combination with the social network graph, be used to predict the attributes of another user in the network? To answer this question, we gather fine-grained data from two social networks and try to infer user profile attributes. We find that users with common attributes are more likely to be friends and often form dense communities, and we propose a method of inferring user attributes that is inspired by previous approaches to detecting communities in social networks. Our results show that certain user attributes can be inferred with high accuracy when given information on as little as 20 % of the users.