spectral analysis for a family of treelike networks abstract for a network knowledge of its laplacian eigenvalues is central to understand its structure and dynamics in this paper we study the laplacian spectra and their applications for a family of treelike networks firstly in order to obtain the laplacian spectra we calculate the constant term and monomial coefficient of characteristic polynomial of the laplacian matrix for a family of treelike networks by using the vieta theorem we then obtain the sum of reciprocals of all nonzero eigenvalues of laplacian matrix finally we determine some interesting quantities that are related to the sum of reciprocals of all nonzero eigenvalues of laplacian matrix such as kirchhoff index global mean first passage time gmfpt

a deterministic small world network created by edge iterations abstract small world networks are ubiquitous in real life systems most previous models of small world networks are stochastic the randomness makes it more difficult to gain a visual understanding on how do different nodes of networks interact with each other and is not appropriate for communication networks that have fixed interconnections here we present a model that generates a small world network in a simple deterministic way our model has a discrete exponential degree distribution we solve the main characteristics of the model

the problem of isomorphy for general discrete memoryless stationary correlated sources necessary and sufficient conditions are given for the isomorphy of discrete memoryless stationary correlated sources with maximal correlation less than 1

random walks in modular scale free networks with multiple traps extensive empirical investigation has shown that a plethora of real networks synchronously exhibit scale free and modular structure and it is thus of great importance to uncover the effects of these two striking properties on various dynamical processes occurring on such networks in this paper we examine two cases of random walks performed on a class of modular scale free networks with multiple traps located at several given nodes we first derive a formula of the mean first passage time mfpt for a general network which is the mean of the expected time to absorption originating from a specific node averaged over all nontrap starting nodes although the computation is complex the expression of the formula is exact moreover the computational approach and procedure are independent of the number and position of the traps we then determine analytically the mfpt for the two random walks being considered the obtained analytical results are in complete agreement with the numerical ones our results show that the number and location of traps play an important role in the behavior of the mfpt since for both cases the mfpt grows as a power law function of the number of nodes but their exponents are quite different we demonstrate that the root of the difference in the behavior of mfpt is attributed to the modular and scale free topologies of the networks this work can deepen the understanding of diffusion on networks with modular and scale free architecture and motivate relevant studies for random walks running on complex random networks with multiple traps

constrained spin dynamics description of random walks on hierarchical scale free networks we study a random walk problem on the hierarchical network which is a scale free network grown deterministically the random walk problem is mapped onto a dynamical ising spin chain system in one dimension with a nonlocal spin update rule which allows an analytic approach we show analytically that the characteristic relaxation time scale grows algebraically with the total number of nodes n as t n z from a scaling argument we also show the power law decay of the autocorrelation function c sigma t t alpha which is the probability to find the ising spins in the initial state sigma after t time steps with the state dependent nonuniversal exponent alpha it turns out that the power law scaling behavior has its origin in a quasiultrametric structure of the configuration space

eigenvalues for the transition matrix of a small world scale free network explicit expressions and applications the eigenvalues of the transition matrix for random walks on a network play a significant role in the structural and dynamical aspects of the network nevertheless it is still not well understood how the eigenvalues behave in small world and scale free networks which describe a large variety of real systems in this paper we study the eigenvalues for the transition matrix of a network that is simultaneously scale free small world and clustered we derive explicit simple expressions for all eigenvalues and their multiplicities with the spectral density exhibiting a power law form we then apply the obtained eigenvalues to determine the mixing time and random target access time for random walks both of which exhibit unusual behaviors compared with those for other networks signaling discernible effects of topologies on spectral features finally we use the eigenvalues to count spanning trees in the network

a geometric growth model interpolating between regular and small world networks we propose a geometric growth model which interpolates between one dimensional linear graphs and small world networks the model undergoes a transition from large to small worlds we study the topological characteristics by both theoretical predictions and numerical simulations which are in good accordance with each other our geometrically growing model is a complementarity for the static ws model

flexible construction of hierarchical scale free networks with general exponent extensive studies have been done to understand the principles behind architectures of real networks recently evidence for hierarchical organization in many real networks has also been reported here we present a hierarchical model that reproduces the main experimental properties observed in real networks scale free of degree distribution p k frequency of the nodes that are connected to k other nodes decays as a power law p k ensuremath sim k ensuremath ensuremath gamma and power law scaling of the clustering coefficient c k ensuremath sim k ensuremath 1 the major points of our model can be summarized as follows a the model generates networks with scale free distribution for the degree of nodes with general exponent ensuremath gamma g2 and arbitrarily close to any specified value being able to reproduce most of the observed hierarchical scale free topologies in contrast previous models cannot obtain values of ensuremath gamma g2 58 b our model has structural flexibility because i it can incorporate various types of basic building blocks e g triangles tetrahedrons and in general fully connected clusters of n nodes and ii it allows a large variety of configurations i e the model can use more than n ensuremath 1 copies of basic blocks of n nodes the structural features of our proposed model might lead to a better understanding of architectures of biological and nonbiological networks

self similar disk packings as model spatial scale free networks the network of contacts in space filling disk packings such as the apollonian packing is examined these networks provide an interesting example of spatial scale free networks where the topology reflects the broad distribution of disk areas a wide variety of topological and spatial properties of these systems is characterized their potential as models for networks of connected minima on energy landscapes is discussed

the structure of isomorphisms of discrete memoryless correlated sources for the class of discrete memoryless stationary correlated sources with non singular dependence and maximal correlation less than 1 it is shown that two such sources can be isomorphic only if there exists a single letter isomorphism between them and they can have only trivial isomorphisms

eigentime identities for random walks on a family of treelike networks and polymer networks abstract in this paper we investigate the eigentime identities quantifying as the sum of reciprocals of all nonzero normalized laplacian eigenvalues on a family of treelike networks and the polymer networks firstly for a family of treelike networks it is shown that all their eigenvalues can be obtained by computing the roots of several small degree polynomials defined recursively we obtain the scalings of the eigentime identity on a family of treelike with network size n n is n n ln n n then for the polymer networks we apply the spectral decimation approach to determine analytically all the eigenvalues and their corresponding multiplicities using the relationship between the generation and the next generation of eigenvalues we obtain the scalings of the eigentime identity on the polymer networks with network size n n is n n ln n n by comparing the eigentime identities on these two kinds of networks their scalings with network size n n are all n n ln n n

acoustic boundary condition for unsteady one dimensional flow calculations abstract a new calculation method is presented that allows the use of the acoustic characteristics of a given singularity as a boundary condition for a non linear one dimensional flow calculation the method is based on the one hand on the non linear decomposition of the pressure perturbation into forward and backward components and on the other hand on the possibility of representing a certain singularity by means of its reflection and transmission coefficients the response of the singularity to the incident pressure components is calculated in the frequency domain and imposed as a boundary condition for the time domain calculation in the rest of the duct the procedure being iterative in this way the calculation takes into account both the acoustic behaviour of the singularity and its interaction with the acoustic source and the rest of the system considered the method is applied to the computation of the flow in the exhaust pipe of a four cylinder spark ignition engine when a complex commercial silencer is used and the results show good agreement with experimental measurements both for in duct pressure and for radiated noise

phase transition in the rich get richer mechanism due to finite size effects the rich get richer mechanism agents increase their wealth randomly at a rate proportional to their holdings is often invoked to explain the pareto power law distribution observed in many physical situations such as the degree distribution of growing scale free nets we use two different analytical approaches as well as numerical simulations to study the case where the number of agents is fixed and finite but large and the rich get richer mechanism is invoked a fraction r of the time the remainder of the time wealth is disbursed by a homogeneous process at short times we recover the pareto law observed for an unbounded number of agents in later times the moving distribution can be scaled to reveal a phase transition with a gaussian asymptotic form for and a pareto like tail on the positive side and a novel stretched exponential decay on the negative side for

the modified box dimension and average weighted receiving time of the weighted hierarchical graph abstract in this paper we study the weighted hierarchical graph which is generated from bipartite graph with n n 1 n 2 vertices in which the weights of edges have been assigned to different values with certain scale firstly we introduce the definition of the modified box dimension then for the weighted hierarchical graph we deduce the modified box dimension dim m b g n n n log r n depending on the weighted factor r and the number n of copies secondly we mainly study their two average weighted receiving times awrts t i n and t ii n of the weighted hierarchical graph on random walk we discuss two cases in the case of n 1 n 2 r n 2 n 1 we deduce both awrts grow as a power law function of the network size v g n with the postive exponent represented by log n n n 1 n 2 or log n r 1 dim m b g n n n which means that the bigger the value of the modified box dimension is the slower the process of receiving information is in the case of n 1 n 2 r n 2 n 1 both awrts tend to constant if n n 1 n 2 the awrts grow with increasing order as log n v g n if n n 1 n 2 and both awrts grow as a power law function of the network size v g n with the exponent represented by log n n n 1 n 2 0 if n n 1 n 2

time domain computation of muffler frequency response comparison of different numerical schemes abstract a comparative study of the performance of different schemes used to solve one dimensional gas flow equations when applied to the computation of the frequency response of exhaust mufflers is presented simple but representative systems with well known acoustic behaviour were considered apart from the classical lax wendroff and maccormack schemes the total variation diminishing schemes flux corrected transport techniques or the innovative space time conservation element and solution element method were considered the results provide guidelines for a proper choice of the numerical scheme taking into account the mesh spacing

a non linear quasi 3d model with flux corrected transport for engine gas exchange modelling modelling has proven to be an important tool in the design of manifolds and silencers for internal combustion engines although simple 1d models are generally sufficiently precise in the case of manifold models they would usually fail to predict the high frequency behaviour of modern compact manifold designs and of course of a complex shaped silencing system complete 3d models are able to account for transversal modes and other non 1d phenomena but at a high computational cost a suitable alternative is provided by time domain non linear quasi 3d models whose computational cost is relatively low but still providing an accurate description of the high frequency behaviour of certain elements in this paper a quasi 3d model which makes use of a non linear second order time and space discretization based on finite volumes is presented as an alternative for avoiding overshoots at discontinuities a flux corrected transport technique has been adapted to the quasi 3d method in order to achieve convergence and avoid numerical dispersion it is shown that the combination of dissipation via damping together with the phoenical form of the anti diffusion term provides satisfactory results

isomorphisms of certain correlated probability spaces and of discrete memoryless correlated sources in an earlier paper 5 we defined a sufficient set of invariants for the isomorphy of discrete memoryless correlated sources with maximal correlation 1 using the structure of isomorphisms of certain correlated probability spaces we give here a sufficient set of invariants also for the case of maximal correlation equal to 1 we show in particular that two discrete memoryless stationary correlated sources with maximal correlation 1 may be isomorphic in a non trivial way

high dimensional apollonian networks we propose a simple algorithm which produces high dimensional apollonian networks with both small world and scale free characteristics we derive analytical expressions for the degree distribution the clustering coefficient and the diameter of the networks which are determined by their dimension

an empirical study of an agglomeration network recently researchers have reported many models mimicking real network evolution growth among which some are based on network aggregation growth however until now relatively few experiments have been reported accordingly in this paper photomicrographs of real materials the agglomeration in the filtrate of slurry formed by a gap nanoparticle conglomerate dispersed in water are analyzed within the framework of complex network theory by data mapping from photomicrographs we generate undirected networks and as a definition of degree we adopt the number of pixel s nearest neighbors while adjacent pixels define a connection or an edge we study the topological structure of these networks including degree distribution clustering coefficient and average path length in addition we discuss the self similarity and synchronizability of the networks we find that the synchronizability of high concentration agglomeration is better than that of low concentration agglomeration we also find that agglomeration networks possess good self similar features

free electron gas in the apollonian network multifractal energy spectrum and its thermodynamic fingerprints we study the free electron gas in an apollonian network within the tight binding framework the scale free and small world character of the underlying lattice is known to result in a quite structured energy spectrum with deltalike singularities gaps and minibands after an exact numerical diagonalization of the corresponding adjacency matrix of the network with a finite number of generations we employ a scaling analysis of the moments of the density of states to characterize its multifractality and report the associated singularity spectrum the fractal nature of the energy spectrum is also shown to be reflected in the thermodynamic behavior by logarithmic modulations on the temperature dependence of the specific heat the absence of chiral symmetry of the apollonian network leads to distinct thermodynamic behaviors due to electrons and holes thermal excitations

formulation and validation of boundary conditions at a branched junction for nonlinear waves abstract a numerical model is presented for the calculation of nonlinear waves through the branched junctions in a gas transmission pipe system in the one dimensional time domain analysis of the wave dynamics the behaviour of the nonlinear waves is determined by quasi steady boundary conditions at junctions in a pipe system the quasi steady treatment through the junction yields a system of nonlinear balance equations the iterative solution procedure of the system of nonlinear equations causes the problems of divergence and multiple solutions in order to overcome the difficulties a new set of quasi linear balance equations is formulated without a sacrifice of accuracy the present model therefore requires a non iterative solution procedure that results in a unique solution and a smaller computational effort thompson s boundary condition is used at each pipe a new time derivative form of balance equations based thompson boundary condition gives a set of linear algebraic equations for the balance equations when implementing the new time derivative form of the balance equations corrected terms are added numerically the present numerical model is implemented and tested for the calculation of behaviour of nonlinear waves in a branched pipe and the calculation of sound attenuation of a helmholtz resonator and the prediction of radiated orifice noise of an internal combustion engine calculation results show good agreements with previous iterative calculations and measurement data

enumeration of spanning trees in planar unclustered networks abstract among a variety of subgraphs spanning trees are one of the most important and fundamental categories they are relevant to diverse aspects of networks including reliability transport self organized criticality loop erased random walks and so on in this paper we introduce a family of modular self similar planar networks with zero clustering relevant properties of this family are comparable to those networks associated with technological systems having low clustering like power grids some electronic circuits the internet and some biological systems so it is very significant to research on spanning trees of planar networks however for a large network evaluating the relevant determinant is intractable in this paper we propose a fairly generic linear algorithm for counting the number of spanning trees of a planar network using the algorithm we derive analytically the exact numbers of spanning trees in planar networks our result shows that the computational complexity is o t which is better than that of the matrix tree theorem with o m 2 t 2 where t is the number of steps and m is the girth of the planar network we also obtain the entropy for the spanning trees of a given planar network we find that the entropy of spanning trees in the studied network is small which is in sharp contrast to the previous result for planar networks with the same average degree we also determine an upper bound and a lower bound for the numbers of spanning trees in the family of planar networks by the algorithm as another application of the algorithm we give a formula for the number of spanning trees in an outerplanar network with small world features

trapping in scale free networks with hierarchical organization of modularity a wide variety of real life networks share two remarkable generic topological properties scale free behavior and modular organization and it is natural and important to study how these two features affect the dynamical processes taking place on such networks in this paper we investigate a simple stochastic process trapping problem a random walk with a perfect trap fixed at a given location performed on a family of hierarchical networks that exhibit simultaneously striking scale free and modular structure we focus on a particular case with the immobile trap positioned at the hub node having the largest degree using a method based on generating functions we determine explicitly the mean first passage time mfpt for the trapping problem which is the mean of the node to trap first passage time over the entire network the exact expression for the mfpt is calculated through the recurrence relations derived from the special construction of the hierarchical networks the obtained rigorous formula corroborated by extensive direct numerical calculations exhibits that the mfpt grows algebraically with the network order concretely the mfpt increases as a power law function of the number of nodes with the exponent much less than 1 we demonstrate that the hierarchical networks under consideration have more efficient structure for transport by diffusion in contrast with other analytically soluble media including some previously studied scale free networks we argue that the scale free and modular topologies are responsible for the high efficiency of the trapping process on the hierarchical networks

application of maccormack schemes to i c engine exhaust noise prediction non linear flow calculations are a usual tool for describing the flow inside intake and exhaust systems of internal combustion engines therefore they may also be used to estimate the noise radiated by these systems most of the work reported in this field is related to the use of the method of characteristics and some references to the use of the lax wendroff finite differences scheme are also found in this paper maccormack predictor corrector schemes are shown to be less dispersive and slightly faster than the lax wendroff scheme and are used to solve the one dimensional flow equations in the case of the exhaust system of a single cylinder engine a modification of the treatment of the source terms is proposed which results in a considerable reduction in the computation time without any loss of information an iterative procedure has been devised that allows the use with this finite differences scheme of boundary conditions developed to be used with the method of characteristics comparison with experimental results is given for the case of an exhaust duct without muffler and with an expansion chamber showing fair agreement in both cases

a class of vertex edge growth small world network models having scale free self similar and hierarchical characters abstract the problem of uncovering the internal operating function of network models is intriguing demanded and attractive in researches of complex networks notice that in the past two decades a great number of artificial models are built to try to answer the above mentioned task based on the different growth ways these previous models can be divided into two categories one type possessing the preferential attachment follows a power law p k k 2 3 the other has exponential scaling feature p k k however there are no models containing above two kinds of growth ways to be presented even the study of interconnection between these two growth manners in the same model is lacking hence in this paper we construct a class of planar and self similar graphs motivated from a new attachment way vertex edge growth network operation more precisely the couple of both them we report that this model is sparse small world and hierarchical and then not only is scale free feature in our model but also lies the degree parameter 3 242 out the typical range note that we suggest that the coexistence of multiple vertex growth ways will have a prominent effect on the power law parameter and the preferential attachment plays a dominate role on the development of networks over time at the end of this paper we obtain an exact analytical expression for the total number of spanning trees of models and also capture spanning trees entropy which we have compared with those of their corresponding component elements

on the hosoya index of a family of deterministic recursive trees abstract in this paper we calculate the hosoya index in a family of deterministic recursive trees with a special feature that includes new nodes which are connected to existing nodes with a certain rule we then obtain a recursive solution of the hosoya index based on the operations of a determinant the computational complexity of our proposed algorithm is o log 2 n with n being the network size which is lower than that of the existing numerical methods finally we give a weighted tree shrinking method as a graphical interpretation of the recurrence formula for the hosoya index

analysis of scale free networks based on a threshold graph with intrinsic vertex weights many real networks are complex and have power law vertex degree distribution short diameter and high clustering we analyze the network model based on thresholding of the summed vertex weights which belongs to the class of networks proposed by caldarelli et al phys rev lett 89 258702 2002 power law degree distributions particularly with the dynamically stable scaling exponent 2 realistic clustering and short path lengths are produced for many types of weight distributions thresholding mechanisms can underlie a family of real complex networks that is characterized by cooperativeness and the baseline scaling exponent 2 it contrasts with the class of growth models with preferential attachment which is marked by competitiveness and baseline scaling exponent 3

prediction of the acoustical performances of muffling pipe systems by the method of characteristics abstract a numerical model is presented for the calculation of sound attenuation of flow duct systems in the frequency domain the method of characteristics is used to solve the non linear hyperbolic problem of plane wave motion in ducts the basic conservation equations are not linearized to achieve a comparison between linear model and gas dynamic model predictions boundary conditions providing acoustic excitation of the duct system are explained and details are given about the calculation of the transfer functions of muffling pipe systems including some numerical algorithms to achieve satisfactory predictions by the method of characteristics end corrections have been introduced to take account of phase shifts in the wave reflection at open terminations as well as at abrupt area changes a comparison between experimental attenuation curves measured in a semi anechoic room and calculated ones is displayed for some simple geometries including helmholtz resonators and expansion chambers and shows a fairly good agreement

effects of triad formations stimulated by intermediaries on network topology abstract triad formation of vertices is considered a significant mechanism in the emergence of highly clustered structures in real networks however the net effect of triad formations on network topology has yet to be understood completely since triad formations are usually studied with additional effects including the attachment of new vertices to prevent a saturation of the number of edges where almost all vertices are directly linked to each other in this paper we focus on the net effects of triad formations stimulated by randomly chosen intermediaries on network topologies such as local clustering and evolution of degrees we show that the local clustering of vertices with degree k is divided into an essential term 1 k which can be widely seen in real networks and additional terms depending on the initial network topology also we derive an equation which measures the influence of local structures of networks on the time evolution of vertex degrees according to which triad formations lead to the so called rich get richer phenomenon in the evolution of degrees local events like a triad formation stimulated by pre existing vertices leads not only to highly clustered structures but to a typical power law form in the degree distribution with a power law exponent of about 2

explicit determination of mean first passage time for random walks on deterministic uniform recursive trees the determination of mean first passage time mfpt for random walks in networks is a theoretical challenge and is a topic of considerable recent interest within the physics community in this paper according to the known connections between mfpt effective resistance and the eigenvalues of graph laplacian we first study analytically the mfpt between all node pairs of a class of growing treelike networks which we term deterministic uniform recursive trees durts since one of its particular cases is a deterministic version of the famous uniform recursive tree the interesting quantity is determined exactly through the recursive relation of the laplacian spectra obtained from the special construction of durts the analytical result shows that the mfpt between all couples of nodes in durts varies as n text text ln text n for large networks with node number n second we study trapping on a particular network of durts focusing on a special case with the immobile trap positioned at a node having largest degree we determine exactly the average trapping time att that is defined as the average of fpt from all nodes to the trap in contrast to the scaling of the mfpt the leading behavior of att is a linear function of n interestingly we show that the behavior for att of the trapping problem is related to the trapping location which is in comparison with the phenomenon of trapping on fractal t graph although both networks exhibit tree structure finally we believe that the methods could open the way to exactly calculate the mfpt and att in a wide range of deterministic media

a family of small world network models built by complete graph and iteration function abstract small world networks are popular in real life complex systems in the past few decades researchers presented amounts of small world models in which some are stochastic and the rest are deterministic in comparison with random models it is not only convenient but also interesting to study the topological properties of deterministic models in some fields such as graph theory theorem computer sciences and so on as another concerned darling in current researches community structure modular topology is referred to as an useful statistical parameter to uncover the operating functions of network so building and studying such models with community structure and small world character will be a demanded task hence in this article we build a family of sparse network space n t which is different from those previous deterministic models even though our models are established in the same way as them iterative generation by randomly connecting manner in each time step every resulting member in n t has no absolutely self similar feature widely shared in a large number of previous models this makes our insight not into discussing a class certain model but into investigating a group various ones spanning a network space somewhat surprisingly our results prove all members of n t to possess some similar characters a sparsity b exponential scale feature p k k and c small world property here we must stress a very screming but intriguing phenomenon that the difference of average path length a p l between any two members in n t is quite small which indicates this random connecting way among members has no great effect on a p l at the end of this article as a new topological parameter correlated to reliability synchronization capability and diffusion properties of networks the number of spanning trees on a representative member n b t of n t is studied in detail then an exact analytical solution for its spanning trees entropy is also obtained

weighted fractal networks abstract in this paper we define a new class of weighted complex networks sharing several properties with fractal sets and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension general networks with fractal or hierarchical structures can be set in the proposed framework that moreover could be used to provide some answers to the widespread emergence of fractal structures in nature

eigentime identities of flower networks with multiple branches abstract for the fractal networks the eigentime identity is the expected time for a walker going from one node to another in this paper we study a family of flower networks that have k parallel paths with lengths m 1 m 2 m k let c t be the eigentime identity of the flower networks in generation t then the obtained result shows that the eigentime identity is c t i 1 k m i i 1 k m i 1 t

experimental validation of a new semi implicit ce se scheme for the calculation of unsteady one dimensional flow in tapered ducts this paper presents an improvement in the conservation element solution element ce se scheme for calculating one dimensional flow through tapered ducts this new ce se scheme has been validated against experiments in tapered ducts with non steady flow using pressure impulses this validation analyses scheme s ability to reproduce instantaneous pressure in time and frequency domains mass conservation when the section of the duct changes which was the main drawback of the original ce se scheme and finally computational time in order to quantify the improvement of the scheme the calculations have been compared with experimental data and with the results provided by other schemes such as the original ce se or total variation diminishing schemes this comparison shows important improvements in mass conservation in relation to the original ce se and not significant penalties in computational time copyright 2007 john wiley sons ltd

structural and spectral properties of a family of deterministic recursive trees rigorous solutions as one of the most significant models the uniform recursive tree urt has found many applications in a variety of fields in this paper we study rigorously the structural features and spectral properties of the adjacency matrix for a family of deterministic uniform recursive trees durts that are deterministic versions of urt firstly from the perspective of complex networks we investigate analytically the main structural characteristics of durts and obtain the accurate solutions for these properties which include degree distribution average path length distribution of node betweenness and degree correlations then we determine the complete eigenvalues and their corresponding eigenvectors of the adjacency matrix for durts our research may shed light on a better understanding of the features for urt also the analytical methods used here are capable of being extended to many other deterministic networks making the precise computation of their properties especially the full spectrum characteristics possible

analysis of diffusion and trapping efficiency for random walks on non fractal scale free trees abstract in this paper the discrete random walks on the recursive non fractal scale free trees nfsft are studied and a kind of method to calculate the analytic solutions of the mean first passage time mfpt for any pair of nodes the mean trapping time mtt for any target node and mean diffusing time mdt for any starting node are proposed furthermore we compare the trapping efficiency and diffusion efficiency between any two nodes of nfsft by using the mtt and the mdt as the measures of trapping efficiency and diffusion efficiency respectively and find the best or worst trapping sites and the best or worst diffusion sites the results show that the two hubs of nfsft are not only the best trapping site but also the worst diffusion site and that the nodes which are the farthest nodes from the two hubs are not only the worst trapping sites but also the best diffusion sites furthermore we find that the ratio between the maximum and minimum of mtt grows logarithmically with network order but the ratio between the maximum and minimum of mdt is almost equal to 1 the results imply that the trap s position has great effect on the trapping efficiency but the position of starting node has little effect on diffusion efficiency finally the simulation for random walks on nfsft is done and it is consistent with the derived results

a key heterogeneous structure of fractal networks based on inverse renormalization scheme abstract self similarity property of complex networks was found by the application of renormalization group theory based on this theory network topologies can be classified into universality classes in the space of configurations in return through inverse renormalization scheme a given primitive structure can grow into a pure fractal network then adding different types of shortcuts it exhibits different characteristics of complex networks however the effect of primitive structure on networks structural property has received less attention in this paper we introduce a degree variance index to measure the dispersion of nodes degree in the primitive structure and investigate the effect of the primitive structure on network structural property quantified by network efficiency numerical simulations and theoretical analysis show a primitive structure is a key heterogeneous structure of generated networks based on inverse renormalization scheme whether or not adding shortcuts and the network efficiency is positively correlated with degree variance of the primitive structure

a small world network derived from the deterministic uniform recursive tree by line graph operation the deterministic uniform recursive tree is one of the deterministic versions of the uniform recursive tree zhang et al 2008 eur phys j b 63 507 13 studied the properties of durt including its topological characteristics and spectral properties although durt shows a logarithmic scaling with the size of the network durt is not a small world network since its clustering coefficient is zero lu et al 2012 physica a 391 87 92 proposed a deterministic small world network by adding some edges with a simple rule in each durt iteration in this paper we intoduce a method for constructing a new deterministic small world network by the line graph operation in each durt iteration the line graph operation brings about cliques at each node of the previous given graph and the resulting line graph possesses larger clustering coefficients on the other hand this operation can decrease the diameter at almost one then giving the analytic solutions to several topological characteristics of the model proposed

a general geometric growth model for pseudofractal scale free web abstract we propose a general geometric growth model for pseudofractal scale free web psw which is controlled by two tunable parameters we derive exactly the main characteristics of the networks degree distribution second moment of degree distribution degree correlations distribution of clustering coefficient as well as the diameter which are partially determined by the parameters analytical results show that the resulting networks are disassortative and follow power law degree distributions with a more general degree exponent tuned from 2 to 1 ln 3 ln 2 the clustering coefficient of each individual node is inversely proportional to its degree and the average clustering coefficient of all nodes approaches to a large nonzero value in the infinite network order the diameter grows logarithmically with the number of network nodes all these reveal that the networks described by our model have small world effect and scale free topology

average weighted receiving time on the non homogeneous double weighted fractal networks abstract in this paper based on actual road networks a model of the non homogeneous double weighted fractal networks is introduced depending on the number of copies s and two kinds of weight factors w i r i i 1 2 s the double weights represent the capacity flowing weights and the cost traveling weights respectively denote by w i j f the capacity flowing weight connecting the nodes i and j and denote by w i j c the cost traveling weight connecting the nodes i and j let w i j f be related to the weight factors w 1 w 2 w s and let w i j c be related to the weight factors r 1 r 2 r s assuming that the walker at each step starting from its current node moves to any of its neighbors with probability proportional to the capacity flowing weight of edge linking them the weighted time for two adjacency nodes is the cost traveling weight connecting the two nodes the average weighted receiving time awrt is defined on the non homogeneous double weighted fractal networks awrt depends on the relationships of the number of copies s and two kinds of weight factors w i r i i 1 2 s the obtained remarkable results display that in the large network the awrt grows as a power law function of the network size n g with the exponent represented by log s w 1 r 1 w 2 r 2 w s r s 1 when w 1 r 1 w 2 r 2 w s r s 1 which means that the smaller the value of w 1 r 1 w 2 r 2 w s r s is the more efficient the process of receiving information is especially when w 1 r 1 w 2 r 2 w s r s 1 awrt grows with increasing order n g as log n g or log n g 2 in the classic fractal networks the average receiving time art grows with linearly with the network size n g thus the non homogeneous double weighted fractal networks are more efficient than classic fractal networks in term of receiving information

geometric fractal growth model for scale free networks we introduce a deterministic model for scale free networks whose degree distribution follows a power law with the exponent ensuremath gamma at each time step each vertex generates its offspring whose number is proportional to the degree of that vertex with proportionality constant m ensuremath 1 mg1 we consider the two cases first each offspring is connected to its parent vertex only forming a tree structure second it is connected to both its parent and grandparent vertices forming a loop structure we find that both models exhibit power law behaviors in their degree distributions with the exponent ensuremath gamma 1 mathrm ln 2m ensuremath 1 mathrm ln m thus by tuning m the degree exponent can be adjusted in the range 2l ensuremath gamma l3 we also solve analytically a mean shortest path distance d between two vertices for the tree structure showing the small world behavior that is d ensuremath sim mathrm ln n mathrm ln overline k where n is system size and overline k is the mean degree finally we consider the case that the number of offspring is the same for all vertices and find that the degree distribution exhibits an exponential decay behavior

scale free networks with a large to hypersmall world transition abstract recently there has been a tremendous interest in models of networks with a power law distribution of degree so called scale free networks it has been observed that such networks normally have extremely short path lengths scaling logarithmically or slower with system size as an exotic and counterintuitive example we propose a simple stochastic model capable of generating scale free networks with linearly scaling distances furthermore by tuning a parameter the model undergoes a phase transition to a regime with extremely short average distances apparently slower than log log n which we call a hypersmall world regime we characterize the degree degree correlation and clustering properties of this class of networks

farey graphs as models for complex networks farey sequences of irreducible fractions between 0 and 1 can be related to graph constructions known as farey graphs these graphs were first introduced by matula and kornerup in 1979 and further studied by colbourn in 1982 and they have many interesting properties they are minimally 3 colorable uniquely hamiltonian maximally outerplanar and perfect in this paper we introduce a simple generation method for a farey graph family and we study analytically relevant topological properties order size degree distribution and correlation clustering transitivity diameter and average distance we show that the graphs are a good model for networks associated with some complex systems

the relations between network operation and topological property in a scale free and small world network with community structure abstract it is always an open demanding and difficult task for generating available model to simulate dynamical functions and reveal inner principles from complex systems and networks in this article due to lots of real life and artificial networks are built from series of simple and small groups components we discuss some interesting and helpful network operation to generate more realistic network models in view of community structure modular topology we present a class of sparse network models n t m at the moment we capture the fact the n t 4 has not only scale free feature which means that the probability that a randomly selected vertex with degree k decays as a power law following p k k where is the degree exponent but also small world property which indicates that the typical distance between two uniform randomly chosen vertices grows proportionally to logarithm of the order of n t 4 namely relatively shorter diameter and lower average path length simultaneously displays higher clustering coefficient next as a new topological parameter correlating to reliability synchronization capability and diffusion properties of networks the number of spanning trees over a network is studied in more detail an exact analytical solution for the number of spanning trees of the n t 4 is obtained based on the network operation part hub vertex linking with each other will be helpful for structuring various network models and investigating the rules related with real life networks

tuning degree distributions departing from scale free networks abstract scale free networks are characterized by a degree distribution with power law behavior although scale free networks have been shown to arise in many areas ranging from the world wide web to transportation or social networks degree distributions of other observed networks often differ from the power law type data based investigations require modifications of the typical scale free network we present an algorithm that generates networks in which the shape of the degree distribution is tunable by modifying the preferential attachment step of the barabasi albert construction algorithm the shape of the distribution is represented by dispersion measures such as the variance and the skewness both of which are highly correlated with the maximal degree of the network and therefore adequately represents the influence of superspreaders or hubs by combining our algorithm with work of holme and kim we show how to generate networks with a variety of degree distributions and clustering coefficients

influences of degree inhomogeneity on average path length and random walks in disassortative scale free networks various real life networks exhibit degree correlations and heterogeneous structure with the latter being characterized by power law degree distribution p k k where the degree exponent describes the extent of heterogeneity in this paper we study analytically the average path length apl of and random walks rws on a family of deterministic networks recursive scale free trees rsfts with negative degree correlations and various 2 1 ln 3 ln 2 with an aim to explore the impacts of structure heterogeneity on the apl and rws we show that the degree exponent has no effect on the apl d of rsfts in the full range of d behaves as a logarithmic scaling with the number of network nodes n i e d ln n which is in sharp contrast to the well known double logarithmic scaling d ln ln n previously obtained for uncorrelated scale free networks with 2 3 in addition we present that some scaling efficiency exponents of random walks are reliant on the degree exponent

degree dependent intervertex separation in complex networks we study the mean length l k of the shortest paths between a vertex of degree k and other vertices in growing networks where correlations are essential in a number of deterministic scale free networks we observe a power law correction to a logarithmic dependence l k a ln n k gamma 1 2 ck gamma 1 n in a wide range of network sizes here n is the number of vertices in the network gamma is the degree distribution exponent and the coefficients a and c depend on a network we compare this law with a corresponding l k dependence obtained for random scale free networks growing through the preferential attachment mechanism in stochastic and deterministic growing trees with an exponential degree distribution we observe a linear dependence on degree l k approximately a ln n ck we compare our findings for growing networks with those for uncorrelated graphs

flux corrected transport this paper describes a class of explicit eulerian finite difference algorithms for solving the continuity equation which are built around a technique called flux correction these flux corrected transport fct algorithms are of indeterminate order but yield realistic accurate results in addition to the mass conserving property of most conventional algorithms the fct algorithms strictly maintain the positivity of actual mass densities so steep gradients and inviscid shocks are handled particularly well this first paper concentrates on a simple one dimensional version of fct utilizing shasta a new transport algorithm for the continuity equation which is described in detail

full eigenvalues of the markov matrix for scale free polymer networks much important information about the structural and dynamical properties of complex systems can be extracted from the eigenvalues and eigenvectors of a markov matrix associated with random walks performed on these systems and spectral methods have become an indispensable tool in the complex system analysis in this paper we study the markov matrix of a class of scale free polymer networks we present an exact analytical expression for all the eigenvalues and determine explicitly their multiplicities we then use the obtained eigenvalues to derive an explicit formula for the random target access time for random walks on the studied networks furthermore based on the link between the eigenvalues of the markov matrix and the number of spanning trees we confirm the validity of the obtained eigenvalues and their corresponding degeneracies

a new data processing inequality and its applications in distributed source and channel coding in the distributed coding of correlated sources the problem of characterizing the joint probability distribution of a pair of random variables satisfying an n letter markov chain arises the exact solution of this problem is intractable in this paper we seek a single letter necessary condition for this n letter markov chain to this end we propose a new data processing inequality on a new measure of correlation through a spectral method based on this new data processing inequality we provide a single letter necessary condition for the required joint probability distribution we apply our results to two specific examples involving the distributed coding of correlated sources multiple access channel with correlated sources and multiterminal rate distortion region and propose new necessary conditions for these two problems

self similar non clustered planar graphs as models for complex networks in this paper we introduce a family of planar modular and self similar graphs which has small world and scale free properties the main parameters of this family are comparable to those of networks associated with complex systems and therefore the graphs are of interest as mathematical models for these systems as the clustering coefficient of the graphs is zero this family is an explicit construction that does not match the usual characterization of hierarchical modular networks namely that vertices have clustering values inversely proportional to their degrees

deterministic weighted scale free small world networks abstract we propose a deterministic weighted scale free small world model for considering pseudofractal web with the co evolution of topology and weight considering the fluctuations in traffic flow constitute a main reason for congestion of packet delivery and poor performance of communication networks we suggest a recursive algorithm to generate the network which restricts the traffic fluctuations on it effectively during the evolutionary process we provide a relatively complete view of topological structure and weight dynamics characteristics of the networks such as weight and strength distribution degree correlations average clustering coefficient and degree cluster correlations as well as the diameter

on the spectra of hypertrees in this paper we study the spectral properties of a family of trees characterized by two main features they are spanning subgraphs of the hypercube and their vertices bear a high degree of connectedness hierarchy such structures are here called binary hypertrees and they can be recursively defined as the so called hierarchical product of several complete graphs on two vertices ams classification 05c50 05c05

analysis of acoustic networks including cavities by means of a linear finite volume method abstract a procedure allowing for the analysis of complex acoustic networks including three dimensional cavities described in terms of zero dimensional equivalent elements is presented and validated the procedure is based on the linearization of the finite volume method often used in gas dynamics which is translated into an acoustic network comprising multi ports accounting for mass exchanges between the finite volumes and equivalent 2 ports describing momentum exchange across the volume surfaces the application of the concept to a one dimensional case shows that it actually converges to the exact analytical solution when a sufficiently large number of volumes are considered this has allowed the formulation of an objective criterion for the choice of a mesh providing results with a prefixed error up to a certain helmholtz number which has been generalized to three dimensional cases the procedure is then applied to simple but relevant three dimensional geometries in the absence of a mean flow showing good agreement with experimental and other computational results