The stability of a graph partition: A dynamics-based framework for community detection

Recent years have seen a surge of interest in the analysis of complex networks, facilitated by the availability of relational data and the increasingly powerful computational resources that can be employed for their analysis. Naturally, the study of real-world systems leads to highly complex networks and a current challenge is to extract intelligible, simplified descriptions from the network in terms of relevant subgraphs, which can provide insight into the structure and function of the overall system. Sparked by seminal work by Newman and Girvan, an interesting line of research has been devoted to investigating modular community structure in networks, revitalising the classic problem of graph partitioning. However, modular or community structure in networks has notoriously evaded rigorous definition. The most accepted notion of community is perhaps that of a group of elements which exhibit a stronger level of interaction within themselves than with the elements outside the community. This concept has resulted in a plethora of computational methods and heuristics for community detection. Nevertheless a firm theoretical understanding of most of these methods, in terms of how they operate and what they are supposed to detect, is still lacking to date. Here, we will develop a dynamical perspective towards community detection enabling us to define a measure named the stability of a graph partition. It will be shown that a number of previously ad-hoc defined heuristics for community detection can be seen as particular cases of our method providing us with a dynamic reinterpretation of those measures. Our dynamics-based approach thus serves as a unifying framework to gain a deeper understanding of different aspects and problems associated with community detection and allows us to propose new dynamically-inspired criteria for community structure.Comment: 3 figures; published as book chapte

Performance evaluation of WMN-GA for different mutation and crossover rates considering number of covered users parameter

Node placement problems have been long investigated in the optimization field due to numerous applications in location science and classification. Facility location problems are showing their usefulness to communication networks, and more especially from Wireless Mesh Networks (WMNs) field. Recently, such problems are showing their usefulness to communication networks, where facilities could be servers or routers offering connectivity services to clients. In this paper, we deal with the effect of mutation and crossover operators in GA for node placement problem. We evaluate the performance of the proposed system using different selection operators and different distributions of router nodes considering number of covered users parameter. The simulation results show that for Linear and Exponential ranking methods, the system has a good performance for all rates of crossover and mutation.Peer ReviewedPostprint (published version

Stability of graph communities across time scales

The complexity of biological, social and engineering networks makes it desirable to find natural partitions into communities that can act as simplified descriptions and provide insight into the structure and function of the overall system. Although community detection methods abound, there is a lack of consensus on how to quantify and rank the quality of partitions. We show here that the quality of a partition can be measured in terms of its stability, defined in terms of the clustered autocovariance of a Markov process taking place on the graph. Because the stability has an intrinsic dependence on time scales of the graph, it allows us to compare and rank partitions at each time and also to establish the time spans over which partitions are optimal. Hence the Markov time acts effectively as an intrinsic resolution parameter that establishes a hierarchy of increasingly coarser clusterings. Within our framework we can then provide a unifying view of several standard partitioning measures: modularity and normalized cut size can be interpreted as one-step time measures, whereas Fiedler's spectral clustering emerges at long times. We apply our method to characterize the relevance and persistence of partitions over time for constructive and real networks, including hierarchical graphs and social networks. We also obtain reduced descriptions for atomic level protein structures over different time scales.Comment: submitted; updated bibliography from v

Network Model Selection Using Task-Focused Minimum Description Length

Networks are fundamental models for data used in practically every application domain. In most instances, several implicit or explicit choices about the network definition impact the translation of underlying data to a network representation, and the subsequent question(s) about the underlying system being represented. Users of downstream network data may not even be aware of these choices or their impacts. We propose a task-focused network model selection methodology which addresses several key challenges. Our approach constructs network models from underlying data and uses minimum description length (MDL) criteria for selection. Our methodology measures efficiency, a general and comparable measure of the network's performance of a local (i.e. node-level) predictive task of interest. Selection on efficiency favors parsimonious (e.g. sparse) models to avoid overfitting and can be applied across arbitrary tasks and representations. We show stability, sensitivity, and significance testing in our methodology

Design and Analysis of SD_DWCA - A Mobility based clustering of Homogeneous MANETs

This paper deals with the design and analysis of the distributed weighted clustering algorithm SD_DWCA proposed for homogeneous mobile ad hoc networks. It is a connectivity, mobility and energy based clustering algorithm which is suitable for scalable ad hoc networks. The algorithm uses a new graph parameter called strong degree defined based on the quality of neighbours of a node. The parameters are so chosen to ensure high connectivity, cluster stability and energy efficient communication among nodes of high dynamic nature. This paper also includes the experimental results of the algorithm implemented using the network simulator NS2. The experimental results show that the algorithm is suitable for high speed networks and generate stable clusters with less maintenance overhead

Minimum-cost multicast over coded packet networks

We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomial-time solvable optimization problem, and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimum-cost multicast. By contrast, establishing minimum-cost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved

Distributed Rate Allocation Policies for Multi-Homed Video Streaming over Heterogeneous Access Networks

We consider the problem of rate allocation among multiple simultaneous video streams sharing multiple heterogeneous access networks. We develop and evaluate an analytical framework for optimal rate allocation based on observed available bit rate (ABR) and round-trip time (RTT) over each access network and video distortion-rate (DR) characteristics. The rate allocation is formulated as a convex optimization problem that minimizes the total expected distortion of all video streams. We present a distributed approximation of its solution and compare its performance against H-infinity optimal control and two heuristic schemes based on TCP-style additive-increase-multiplicative decrease (AIMD) principles. The various rate allocation schemes are evaluated in simulations of multiple high-definition (HD) video streams sharing multiple access networks. Our results demonstrate that, in comparison with heuristic AIMD-based schemes, both media-aware allocation and H-infinity optimal control benefit from proactive congestion avoidance and reduce the average packet loss rate from 45% to below 2%. Improvement in average received video quality ranges between 1.5 to 10.7 dB in PSNR for various background traffic loads and video playout deadlines. Media-aware allocation further exploits its knowledge of the video DR characteristics to achieve a more balanced video quality among all streams.Comment: 12 pages, 22 figure

On-demand Bandwidth and Stability Based Unicast Routing in Mobile Adhoc Networks

Characteristics of mobile ad hoc networks (MANETs) such as lack of central coordination, dynamic topology and limited resources pose a challenging problem in quality of service (QoS) routing. Providing an efficient, robust and low overhead QoS unicast route from source to destination is a critical issue. Bandwidth and route stability are the major important QoS parameters for applications where long duration connections are required with stringent bandwidth requirements for multimedia applications. This paper proposes an On-demand Bandwidth and Stability based Unicast Routing scheme (OBSUR) in MANET by adding additional QoS features to existing Dynamic Source Routing (DSR) protocol. The objective of the OBSUR is to provide QoS satisfied, reliable and robust route for communicating nodes. The scheme works in following steps. (1) Each node in the network periodically (small regular intervals) estimates bandwidth availability, node and link stability, buffer availability, and stability factor between nodes. (2) Construction of neighbor stability and QoS database at every node which is used in route establishment process. (3) The unicast path is constructed by using route request and route reply packets with the help of route information cache, and (4) route maintenance in case of node mobility and route failures. Simulation results show that there is an improvement in terms of traffic admission ratio, control overhead, packet delivery ratio, end to end delay and throughput as compared to Route Stability Based QoS Routing (RSQR) in MANETs.

Identified the Cluster Based Stretch and Shrink Method Based On Load Balancing Algorithm for Ad Hoc Network Topology Stability

No Abstrac