A network function-based definition of communities in complex networks

2012 ◽  
Vol 22 (3) ◽  
pp. 033129 ◽  
Author(s):  
Sanjeev Chauhan ◽  
Michelle Girvan ◽  
Edward Ott
Keyword(s):  
Complex Networks ◽  
Network Function ◽  
Definition Of

scholarly journals Convexity in complex networks

2018 ◽  
Vol 6 (2) ◽  
pp. 176-203 ◽  
Author(s):  
TILEN MARC ◽  
LOVRO ŠUBELJ
Keyword(s):  
Complex Networks ◽  
Geodesic Distance ◽  
Connected Subgraph ◽  
Geodesic Path ◽  
Connected Subset ◽  
Social Collaboration ◽  
Graph Properties ◽  
Definition Of ◽  
Locally Convex ◽  
Convex Core

AbstractMetric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes of the subgraph lies entirely within the subgraph. According to our perception of convexity, convex network is such in which every connected subset of nodes induces a convex subgraph. We show that convexity is an inherent property of many networks that is not present in a random graph. Most convex are spatial infrastructure networks and social collaboration graphs due to their tree-like or clique-like structure, whereas the food web is the only network studied that is truly non-convex. Core–periphery networks are regionally convex as they can be divided into a non-convex core surrounded by a convex periphery. Random graphs, however, are only locally convex meaning that any connected subgraph of size smaller than the average geodesic distance between the nodes is almost certainly convex. We present different measures of network convexity and discuss its applications in the study of networks.

scholarly journals A Potential Information Capacity Index for Link Prediction of Complex Networks Based on the Cannikin Law

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 863 ◽  
Author(s):  
Xing Li ◽  
Shuxin Liu ◽  
Hongchang Chen ◽  
Kai Wang
Keyword(s):  
Complex Networks ◽  
Information Transmission ◽  
Link Prediction ◽  
Information Capacity ◽  
Prediction Methods ◽  
Transmission Process ◽  
Capacity Index ◽  
Definition Of ◽  
Definition Of Information ◽  
Transmission Capability

Recently, a number of similarity-based methods have been proposed for link prediction of complex networks. Among these indices, the resource-allocation-based prediction methods perform very well considering the amount of resources in the information transmission process between nodes. However, they ignore the information channels and their information capacity in information transmission process between two endpoints. Motivated by the Cannikin Law, the definition of information capacity is proposed to quantify the information transmission capability between any two nodes. Then, based on the information capacity, a potential information capacity (PIC) index is proposed for link prediction. Empirical study on 15 datasets has shown that the PIC index we proposed can achieve a good performance, compared with eight mainstream baselines.

VULNERABILITY AND FALL OF EFFICIENCY IN COMPLEX NETWORKS: A NEW APPROACH WITH COMPUTATIONAL ADVANTAGES

2009 ◽  
Vol 19 (02) ◽  
pp. 727-735 ◽  
Author(s):  
S. BOCCALETTI ◽  
R. CRIADO ◽  
J. PELLO ◽  
M. ROMANCE ◽  
M. VELA-PÉREZ
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
New Approach ◽  
And Performance ◽  
Definition Of

An efficient and computationally advantageous definition of vulnerability of a complex network is introduced, through which one is able to overcome a series of practical difficulties encountered by the measurements used so far to quantify a network's security and stability under the effects of failures, attacks or disfunctions. By means of this approach, we prove a series of theorems that allow to gather information on the ranking of the nodes of a network with respect to their strategic importance in order to preserve the functioning and performance of the network as a whole.

scholarly journals Detecting different topologies immanent in scale-free networks with the same degree distribution

2019 ◽  
Vol 116 (14) ◽  
pp. 6701-6706 ◽  
Author(s):  
Dimitrios Tsiotas
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Network Topology ◽  
Degree Distribution ◽  
Growth Process ◽  
Preferential Attachment ◽  
Self Similarity ◽  
Scale Free ◽  
Scale Free Networks ◽  
Definition Of

The scale-free (SF) property is a major concept in complex networks, and it is based on the definition that an SF network has a degree distribution that follows a power-law (PL) pattern. This paper highlights that not all networks with a PL degree distribution arise through a Barabási−Albert (BA) preferential attachment growth process, a fact that, although evident from the literature, is often overlooked by many researchers. For this purpose, it is demonstrated, with simulations, that established measures of network topology do not suffice to distinguish between BA networks and other (random-like and lattice-like) SF networks with the same degree distribution. Additionally, it is examined whether an existing self-similarity metric proposed for the definition of the SF property is also capable of distinguishing different SF topologies with the same degree distribution. To contribute to this discrimination, this paper introduces a spectral metric, which is shown to be more capable of distinguishing between different SF topologies with the same degree distribution, in comparison with the existing metrics.

scholarly journals Community Clustering Algorithm in Complex Networks Based on Microcommunity Fusion

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Jin Qi ◽  
Fei Jiang ◽  
Xiaojun Wang ◽  
Bin Xu ◽  
Yanfei Sun
Keyword(s):  
Complex Networks ◽  
Clustering Algorithm ◽  
Test Results ◽  
Solution Quality ◽  
Data Set ◽  
Community Mining ◽  
Effectiveness And Efficiency ◽  
Definition Of ◽  
Community Clustering ◽  
Mining Algorithms

With the further research on physical meaning and digital features of the community structure in complex networks in recent years, the improvement of effectiveness and efficiency of the community mining algorithms in complex networks has become an important subject in this area. This paper puts forward a concept of the microcommunity and gets final mining results of communities through fusing different microcommunities. This paper starts with the basic definition of the network community and appliesExpansionto the microcommunity clustering which provides prerequisites for the microcommunity fusion. The proposed algorithm is more efficient andhas higher solution qualitycompared with other similar algorithms through the analysis of test results based on network data set.

scholarly journals Finite-Time Passivity of Stochastic Coupled Complex Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Xunwu Yin ◽  
Min Cao
Keyword(s):  
Complex Networks ◽  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Time Varying Delay ◽  
New Concepts ◽  
Definition Of ◽  
Varying Delay

The finite-time passivity problem is, respectively, investigated for stochastic coupled complex networks (SCCNs) with and without time-varying delay. Firstly, we present several new concepts about finite-time passivity in the sense of expectation on the basis of existing passivity definition. By designing appropriate controllers, the finite-time passivity of SCCNs with and without time-varying delay is obtained. In addition, the definition of finite-time synchronization in the sense of expectation is proposed. Under some sufficient conditions and designed controllers, finite-time passivity derives finite-time synchronization. Finally, two examples are given to demonstrate the effectiveness of finite-time passive and synchronization criteria.

scholarly journals Generalized Erdős numbers for network analysis

2018 ◽  
Vol 5 (8) ◽  
pp. 172281
Author(s):  
Greg Morrison ◽  
Levi H. Dudte ◽  
L. Mahadevan
Keyword(s):  
Network Analysis ◽  
Complex Networks ◽  
Strongly Correlated ◽  
Epidemic Spreading ◽  
New Methods ◽  
Finite Resource ◽  
The Mean ◽  
Definition Of ◽  
Topological Proximity ◽  
Non Locality

The identification of relationships in complex networks is critical in a variety of scientific contexts. This includes the identification of globally central nodes and analysing the importance of pairwise relationships between nodes. In this paper, we consider the concept of topological proximity (or ‘closeness’) between nodes in a weighted network using the generalized Erdős numbers (GENs). This measure satisfies a number of desirable properties for networks with nodes that share a finite resource. These include: (i) real-valuedness, (ii) non-locality and (iii) asymmetry. We show that they can be used to define a personalized measure of the importance of nodes in a network with a natural interpretation that leads to new methods to measure centrality. We show that the square of the leading eigenvector of an importance matrix defined using the GENs is strongly correlated with well-known measures such as PageRank, and define a personalized measure of centrality that is also well correlated with other existing measures. The utility of this measure of topological proximity is demonstrated by showing the asymmetries in both the dynamics of random walks and the mean infection time in epidemic spreading are better predicted by the topological definition of closeness provided by the GENs than they are by other measures.

scholarly journals CLUSTERING METHODS IN LARGE-SCALE SYSTEMS

2020 ◽  
Vol 6 (5) ◽  
pp. 21-24
Author(s):  
Denis V. Gadasin ◽  
◽  
Andrey V. Shvedov ◽  
Alyona A. Yudin ◽  
◽  
...  
Keyword(s):  
Social Network ◽  
Complex Networks ◽  
Large Scale ◽  
Physical Nature ◽  
Clustering Methods ◽  
Large Scale Systems ◽  
Practical Applications ◽  
System Properties ◽  
Definition Of ◽  
And Training

Interactions between people, groups, organizations, and biological cells have a relationship character that can be represented as a network. The system properties of such networks, regardless of their physical nature, but clearly determining the performance of networks, create the totality of the real world. Complex networks – are naturally existing networks (graphs) that have complex topological properties. The researchers who participate and also make discoveries in this field come from various Sciences such as mathematics, computer science, physics, sociology, and engineering. Therefore, the results of research carry both theoretical knowledge and practical applications in these Sciences. This paper discusses the definition of complex networks. The main characteristics of complex networks, such as clustering and congestion, are considered. A popular social network is considered as a complex network. The calculation of nodes and links of the considered social network is made. The main types of AI development and training are highlighted.

GRAPH ZETA FUNCTION AND DIMENSION OF COMPLEX NETWORK

2007 ◽  
Vol 21 (11) ◽  
pp. 639-644 ◽  
Author(s):  
O. SHANKER
Keyword(s):  
Statistical Mechanics ◽  
Complex Networks ◽  
Zeta Function ◽  
Complex Network ◽  
System Behavior ◽  
Mathematical Properties ◽  
Scaling Property ◽  
Definition Of

In a recent paper we had defined the dimension of a complex network in terms of the scaling property of the volume. The question assumes significance because the dependence of system behavior on dimension is an important topic in statistical mechanics. Hence we consider the definition in more detail, and we propose a more widely applicable definition in this work. This definition has good mathematical properties, and it is based on the definition of a zeta function for complex networks.

Link Prediction in Complex Networks

2020 ◽  
pp. 1196-1236
Author(s):  
Manisha Pujari ◽  
Rushed Kanawati
Keyword(s):  
Complex Networks ◽  
Link Prediction ◽  
Class Imbalance ◽  
Rank Aggregation ◽  
General Description ◽  
Multiplex Network ◽  
Community Information ◽  
Target Network ◽  
Definition Of ◽  
Prediction Approach

This chapter presents the problem of link prediction in complex networks. It provides general description, formal definition of the problem and applications. It gives a state-of-art of various existing link prediction approaches concentrating more on topological approaches. It presents the main challenges of link prediction task in real networks. There is description of our new link prediction approach based on supervised rank aggregation and our attempts to deal with two of the challenges to improve the prediction results. One approach is to extend the set of attributes describing an example (pair of nodes) calculated in a multiplex network that includes the target network. Multiplex networks have a layered structure, each layer having different kinds of links between same sets of nodes. The second way is to use community information for sampling of examples to deal with the problem of class imbalance. All experiments have been conducted on real networks extracted from well-known DBLP bibliographic database.

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