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Register a new userTowards the cycle structures in complex network: A new perspective
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Stars and cycles are basic structures in network construction. The former has been well studied in network analysis, while the latter attracted rare attention. A node together with its neighbors constitute a neighborhood star-structure where the basic assumption is two nodes interact through their direct connection. A cycle is a closed loop with many nodes who can influence each other even without direct connection. Here we show their difference and relationship in understanding network structure and function. We define two cycle-based node characteristics, namely cycle number and cycle ratio, which can be used to measure a nodes importance. Numerical analyses on six disparate real networks suggest that the nodes with higher cycle ratio are more important to network connectivity, while cycle number can better quantify a node influence of cycle-based spreading than the common star-based node centralities. We also find that an ordinary network can be converted into a hypernetwork by considering its basic cycles as hyperedges, meanwhile, a new matrix called the cycle number matrix is captured. We hope that this paper can open a new direction of understanding both local and global structures of network and its function.
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This letter propose a new model for characterizing traffic dynamics in scale-free networks. With a replotted road map of cities with roads mapped to vertices and intersections to edges, and introducing the road capacity L and its handling ability at intersections C, the model can be applied to urban traffic system. Simulations give the overall capacity of the traffic system which is quantified by a phase transition from free flow to congestion. Moreover, we report the fundamental diagram of flow against density, in which hysteresis is found, indicating that the system is bistable in a certain range of vehicle density. In addition, the fundamental diagram is significantly different from single-lane traffic model and 2-D BML model with four states: free flow, saturated flow, bistable and jammed.
A key measure that has been used extensively in analyzing complex networks is the degree of a node (the number of the nodes neighbors). Because of its discrete nature, when the degree measure was used in analyzing weighted networks, weights were either ignored or thresholded in order to retain or disregard an edge. Therefore, despite its popularity, the degree measure fails to capture the disparity of interaction between a node and its neighbors. We introduce in this paper a generalization of the degree measure that addresses this limitation: the continuous node degree (C-degree). The C-degree of a node reflects how many neighbors are effectively being used, taking interaction disparity into account. More importantly, if a node interacts uniformly with its neighbors (no interaction disparity), we prove that the C-degree of the node becomes identical to the nodes (discrete) degree. We analyze four real-world weighted networks using the new measure and show that the C-degree distribution follows the power-law, similar to the traditional degree distribution, but with steeper decline. We also show that the ratio between the C-degree and the (discrete) degree follows a pattern that is common in the four studied networks.
Networks representing complex systems in nature and society usually involve multiple interaction types. These types suggest essential information on the interactions between components, but not all of the existing types are usually discovered. Therefore, detecting the undiscovered edge types is crucial for deepening our understanding of the network structure. Although previous studies have discussed the edge label detection problem, we still lack effective methods for uncovering previously-undetected edge types. Here, we develop an effective technique to detect undiscovered new edge types in networks by leveraging a novel temporal network model. Both analytical and numerical results show that the prediction accuracy of our method is perfect when the model networks time parameter approaches infinity. Furthermore, we find that when time is finite, our method is still significantly more accurate than the baseline.
We study the self-organization of the consonant inventories through a complex network approach. We observe that the distribution of occurrence as well as cooccurrence of the consonants across languages follow a power-law behavior. The co-occurrence network of consonants exhibits a high clustering coefficient. We propose four novel synthesis models for these networks (each of which is a refinement of the earlier) so as to successively match with higher accuracy (a) the above mentioned topological properties as well as (b) the linguistic property of feature economy exhibited by the consonant inventories. We conclude by arguing that a possible interpretation of this mechanism of network growth is the process of child language acquisition. Such models essentially increase our understanding of the structure of languages that is influenced by their evolutionary dynamics and this, in turn, can be extremely useful for building future NLP applications.
Cycles, which can be found in many different kinds of networks, make the problems more intractable, especially when dealing with dynamical processes on networks. On the contrary, tree networks in which no cycle exists, are simplifications and usually allow for analyticity. There lacks a quantity, however, to tell the ratio of cycles which determines the extent of network being close to tree networks. Therefore we introduce the term Cycle Nodes Ratio (CNR) to describe the ratio of number of nodes belonging to cycles to the number of total nodes, and provide an algorithm to calculate CNR. CNR is studied in both network models and real networks. The CNR remains unchanged in different sized Erdos Renyi (ER) networks with the same average degree, and increases with the average degree, which yields a critical turning point. The approximate analytical solutions of CNR in ER networks are given, which fits the simulations well. Furthermore, the difference between CNR and two-core ratio (TCR) is analyzed. The critical phenomenon is explored by analysing the giant component of networks. We compare the CNR in network models and real networks, and find the latter is generally smaller. Combining the coarse-graining method can distinguish the CNR structure of networks with high average degree. The CNR is also applied to four different kinds of transportation networks and fungal networks, which give rise to different zones of effect. It is interesting to see that CNR is very useful in network recognition of machine learning.
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