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Information dissemination has become one of the most important services of communication networks. Modeling the diffusion of information through such networks is crucial for our modern information societies. In this work, novel models, segregating between useful and malicious types of information, are introduced, in order to better study Information Dissemination Dynamics (IDD) in wireless complex communication networks, and eventually allow taking into account special network features in IDD. According to the proposed models, and inspired from epidemiology, we investigate the IDD in various complex network types through the use of the Susceptible-Infected (SI) paradigm for useful information dissemination and the Susceptible-Infected-Susceptible (SIS) paradigm for malicious information spreading. We provide analysis and simulation results for both types of diffused information, in order to identify performance and robustness potentials for each dissemination process with respect to the characteristics of the underlying complex networking infrastructures. We demonstrate that the proposed approach can generically characterize IDD in wireless complex networks and reveal salient features of dissemination dynamics in each network type, which could eventually aid in the design of more advanced, robust, and efficient networks and services.

Information dissemination is a key social process in modern information-centric societies, and most of the communication infrastructures have been developed in the last thirty years mainly to allow transferring diverse types of information. Different information types range in scope (e.g., academic, educational, financial, and military), criticality (e.g., confidential, sensitive, public information, etc.), and value (e.g., useful, harmful, and indifferent).

Recent advances in networking have been stimulated in order to accommodate emerging trends of increasing volumes and service demands of disseminated information. In general, information may be distinguished in three types, characterized by useful, malicious, or indifferent content. The first may consist of news, multimedia, or financial data. People are willing to accept such information, and usually such data is stored for further use, for example, e-books. Consequently, it is obtained once, and a user experiences a single transition from the state of not having it to the state of having received the information. On the other hand, users may get malicious information, such as malware, which however are in principle reluctant to accept and/or use. Unfortunately, sources of malicious information manage to devise new ways of spreading such data, for example, through emails, viruses, and trapped websites, so that malicious content is characterized by recurrent behavior, which costs time and money. In addition, the latter holds for indifferent types of information, such as spam email. The user usually discards such information, but relevant messages are of recurrent nature, for example, consisting of repeated or newer phishing messages.

In this work, we focus especially on information dissemination in wireless complex communication networks. Modern networks consist of various complex subnetworks [

Contemporary wireless complex communication network architecture presenting cumulatively all considered types of networks, including interconnections to wired backhauls.

Substantial works [

The main contribution of our work is in realizing that different dynamics are governing the propagation of different types of information and provide appropriate models for each case. Specifically, with regard to useful data, the objective is to spread such information to as many users as possible, so that useful information reaches potentially all nodes of a network. On the contrary, in the event of malicious/indifferent information spreading, the objective is to study the robustness of various network types against harmful or indifferent, but nevertheless network-stressing content. To address the above, in this paper we propose two different paradigms that describe the behavior of systems, a Susceptible Infected (SI) for the first and Susceptible-Infected-Susceptible (SIS) for the second and third types of information. Both paradigms were inspired by drawing analogies to the field of epidemics [

The rest of this paper is organized as follows. In Section

Information dissemination modeling has attracted significant attention the past years, with numerous of works attempting to provide accurate and effective models for modeling the spreading of information, many of which have focused on wireless networks from as early as 1999, [

More specifically, considerably different dynamics govern the propagation of useful and malicious/indifferent types of information. Regarding the spreading process, the dissemination of useful information resembles that of an epidemic disease, in which population members that get infected by a virus, permanently transit to immunization (after recovery), or termination (if the infection is lethal). In epidemics, such models are readily referred to as Susceptible Infected (SI) [

Recognizing the similarities between IDD and the spread of infectious diseases, ODE models in the field of epidemic [

The dissemination of useful information resembles the SI process in epidemics, since a rational user waits to receive desired or useful information and then stores it for further use. If the information is indeed useful and valid, no further transaction for this information will be required/take place. Thus, the user experiences a single state transition when (s)he receives useful information from the noninformed state (node can potentially receive data, i.e., susceptible) to the informed state (i.e., infected). Several works have provided epidemic-based models for such type of information dissemination in the Internet [

This is not the case however in malicious/indifferent information dissemination. Regarding malicious information spreading, users are reluctant to retain the malicious information they receive. However, malicious information might return (if the user is not properly protected), or adversaries are capable of devising a new malware type or package for the malicious information. With respect to indifferent information, even though it is usually of no interest to users, it might further load an already stressed infrastructure, and especially in the case of spam, its repetitive nature might eventually become disturbing, similarly to malware. Consequently, one may consider indifferent information as a special case of malware with respect to the users’ macroscopic behavior. In our treatment, we will employ this observation, due to the fact that we will focus on modeling the macroscopic behavior of IDD. In the following, we will use the terms “malicious” and “indifferent information” interchangeably.

In principle, a user is able to recover (i.e., dispose malicious information) and return to the previous state, where it is possible to become infected again. This behavior resembles epidemics, where individuals become infected, then recover from a disease, and become susceptible again to a different or the same disease (the latter if they do not properly “vaccinate”). Such model is denoted by Susceptible-Infected-Susceptible (SIS) in epidemics [

In summary, compared to previous works, in this paper we introduce two analogies between epidemics and information dissemination. We employ the SI model to describe the macroscopic behavior of useful IDD and the SIS model for malicious (indifferent) IDD. In Sections

In network science (complex network theory) [

As it will be shown in the sequel, by employing the aforementioned analogy to epidemics, IDD can be effectively described and mathematically analyzed for different types of complex communication networks and their topologies. Each network type is characterized by different topological features, and the proposed approach allows in both cases of useful and malicious information identifying the impact of each topology on the IDD performance and robustness. The evaluation of these models will be based on the following critical parameters involved.

Additional properties may be identified, capturing topological properties of the underlying complex networking infrastructures, and could be exploited for analyzing IDD in such networks. The clustering coefficient (indicative of the clusters building up due to social or other types of interaction) and the average path length between randomly selected node pairs are appropriate quantities [

Complex network classification.

Connectivity mixing type | Partially connectible | Equally connectible | Unequally connectible |
---|---|---|---|

Homogeneous mixing | Lattice network, |
ER network | Small-world network |

Heterogeneous mixing | Machine-to-machine network, |
Scale-free network |

Table

As we explained before, the macroscopic behavior of useful information dissemination can be described by the SI epidemic model, in which nodes receive the designated data once in their lifetime. In this section, we provide an analytical approach for quantifying the process of useful information dissemination in various types of complex communication networks.

We adopt the SI model [

We adopt infection parameter

Expressed mathematically, if

The static network is regarded as a time-invariant graph

IDD in regular lattice (HoMPC;

We also observe an interesting phenomenon for the IDD in scale-free networks generated by the BA model. The corresponding IDD curve exceeds that of the SI model in the beginning, but at some instance

Regarding small-world networks, effects of different rewiring probabilities

To overcome the above discussed discrepancies between the SI model and the proposed epidemic IDD model in complex networks, the emerging “degree correlation” problems need to be addressed. The traditional SI model implicitly assumes that each node is uncorrelated. However, when a node is informed in a static network, this suggests that at least one of its neighbors has been informed, and hence the mean degree has to be corrected accordingly. Specifically, the average number of susceptible neighbors of an infected node is less than

For a saturated and HoMEC network given the informed rate

By setting appropriate values of

For a saturated and homogeneous mixing network, the time

As the cumulative informed fraction approaches 1 in a saturated network, Observation

This section discusses the dynamic case where network topology changes with time, while maintaining the basic structure and properties. As it will be shown, a time-varying topology provides great chances for information dissemination to the entire network, and therefore it is suitable for describing complicated interactions within large-scale networks with mobility support (e.g., routing protocols in MANET). Two nodes, originally disconnected, might eventually establish a virtual link between them due to mobility, thus yielding a virtual giant component. Given the condition that a network is originally nonsaturated (e.g., MANET in sparsely populated area), mobility may make the network

A dynamic network is virtually saturated in the sense that the virtual giant component size approaches the number of nodes.

The mobility of nodes facilitates connectivity in homogeneous mixing networks originally not saturated and thus dynamic HoMEC, HoMPC, and HoMUC networks are virtually saturated. In the following, we focus on and analyze IDD in such networks where benefits from mobility are more obvious.

The IDD of dynamic homogeneous mixing networks can be characterized by the corrected SI model.

Due to the virtual saturation property in Observation

To show the significance of these observations and the flexibility of the proposed model, Figure ^{2} plane with wrap-around condition. According to a stationary and ergodic mobility model, such as the Truncated Levy-walk model [

IDD in dynamic MANET with

When nodes are capable of communicating with each other using multiple heterogeneous connections, a hybrid complex network consisting of multiple complex subnetworks is built via heterogeneous links. As in the example we mentioned in Section

The IDD in wireless complex networks (cyber-physical systems) consisting of both long-range and broadcast dissemination patterns.

According to the proposed categories, we exploit ER network (HoMEC) and sensor network (HoMPC) to, respectively, model the delocalized and broadcasting dissemination patterns. Thus, the subpopulation function

When an informed node intends to disseminate via broadcasting, it first scans to search the nearby nodes within its transmission range

Without loss of generality, we assume that a single informed circle is generated at time

To validate the analytical model, we develop experiments to simulate IDD in a hybrid network among 2000 individuals uniformly deployed in a 50 × 50 plane. The constructions of social contact networks and setup of parameters (e.g.,

IDD in hybrid (HoMEC and HoMPC) complex networks of propagating information in both delocalized and broadcast fashions, where

In this section, we adopt and extend an analytical model which is able to capture the behavior of malicious IDD (modeled as SIS epidemics) in wireless multihop networks. Contrary to the case of useful information, regarding malicious/indifferent information, one is interested in the robustness capabilities of the network to sustain such traffic, which in both cases is of no use (even harmful for malware). The proposed analytical model is based on queuing theory, and we apply it on various types of complex wireless networks, as shown cumulatively in Table

In the SIS paradigm, susceptible (noninformed) nodes essentially wait until the arrival of malicious information, in which case they transition to the infected (informed) state. We consider a propagative network, where nodes spread further the malicious information they receive. Consequently, a node might become infected from malicious software either from an attacker or an already infected legitimate node. This holds for several types of viruses and worms that have appeared [

Legitimate nodes can be separated at any instance in two subsets, that is, infected and susceptible. Following the aforementioned modeling approach, the operation of the system can be mapped to a closed two-queue packet network, as shown in Figure

Closed queuing model for SIS malicious information propagative networks.

At any instance, if

Standard approaches from queuing theory may be employed to analyze the two queue closed network. The focus is on the infected queue. Its steady state distribution, denoted by ^{−3}).

Expression (

Based on such model, the expected number of infected (informed) nodes (corresponding to the expected number of packets in the lower queue) for different types of networks may be obtained. The general expression yielded is

Observing the analytic form of the average number of infected nodes for each network type, according to the specific expression of

Contrary to the SI model, in the SIS paradigm employed for the malicious information spreading, average quantities are of interest, while in the SI model instantaneous quantities were considered; as in the long run the network converges to a pandemic (all nodes are informed) state. Particularly, the average number of infected legitimate nodes is the most important quantity, since malicious information is of recurrent nature, and if one observes the system macroscopically, nodes oscillate between the {S}, {I} states.

Figure

Average number of infected users of the legitimate network as a function of

With respect to ad hoc networks (HeMPC), the greatest the transmission radius of nodes, the denser the network, and thus the easier it is for the malicious data to spread. Especially for ad hoc networks, the dependence of the average number of infected nodes on the number of legitimate nodes is linear as shown in Figure

Average number of infected nodes versus

Similar to HeMPC networks, on average in ER networks, the greatest the probability that two nodes are connected (and thus the denser the network is), the easier it becomes for malicious information to propagate. Such property may be also identified with the rest of the network types, leading to the following.

The denser a network becomes, irrespective of its type, the easier for malicious information to spread.

For regular ER, WS, and BA networks with the same

Topological randomness favors the spreading of malicious software.

Among similar network types, the relative (local) density of each topology determines the robustness of the system against malicious information spreading.

In this work, we introduced novel epidemic-based models for modeling and understanding information dissemination dynamics (IDD) in wireless complex networks. Our approach was inspired by epidemic approaches, developed for the study of viruses in social communities. Useful information dissemination was modeled according to the SI epidemic model, while malicious and indifferent types of propagated information were modeled according to the SIS infection paradigm. We provided analytical approaches for obtaining the behavior of spreading dynamics in both paradigms and in order to characterize the spreading of information in specific and diverse types of wireless complex networks. Numerical results depicted the effectiveness of the proposed approaches for analyzing and utilizing the developed processes in the described environment, yielding the most important characteristics of complex networks that affect and control the propagation process. Useful directions were identified for similar studies and developing practical countermeasures/infrastructures.

The proposed methodology and the respective analytical results could be further exploited for defining more complex and application-oriented problems that arise in information diffusion processes in wireless complex networks. For instance, these could be used in order to optimize the spreading of useful information and designing more robust networks capable of sustaining large-scale attacks of malicious spreading information. Depending on the context of each application, more effective dissemination campaigns can be designed and more robust infrastructures developed against malicious intentions.