Recent advances in networking infrastructures and services developed have been partially stimulated in order to accommodate the emerging trends of increasing volumes and service demands of disseminated information, in conjunction with the diversity of information types, as explained above. In general, with respect to the manner that each piece of information is received by human users, information may be distinguished in three types, characterized of useful, malicious, or indifferent content and denoted accordingly. Each type is analyzed in more detail in the following.

Useful information consists of many diverse types of data, all of which are expected to be of some immediate or later use by the end-users. It may consist of news, multimedia content, financial, healthcare, educational data, etc. People are willing to accept such types of information, and usually store it for further use, e.g. e-books and health examinations. Consequently, with respect to useful information, a single state transition takes place for a user, namely, from the state of not having it to the state of having received and stored the information.

On the other hand, users may receive malicious information, most prominently malware. The users are, in principle, reluctant to accept and/or use this type of information. Frequently, the producers and distributors of malicious information devise ways to have their information accepted by some users, e.g. by hiding it in other types of useful or indifferent information, such as email viruses. Furthermore, the sources of malicious information also manage to devise new ways of spreading such data, by using hybrid diffusion means, alternating transmission channels they distribute their threats, and in general discovering new well-hidden methods for entrapping their victims. The net result of this trend is that malicious content is characterized by recurrent behavior, i.e. by a SIS diffusion model explained in the previous chapters. Users will eventually find a way to remove the currently diffusing malware. However, and depending on their level of acquaintance, they will become prone to become infected by the same or new malware that will disseminate in the network at a future time. This of course costs in time and money to the end-users that become victims.

Finally, indifferent information describes cumulatively multiple and diverse types of information that disseminates in societies, nowadays mostly through the Internet and social networks, that the user is not willing to follow, but at the same time the user does not consider harmful. Characteristic cases of indifferent information include spam email (typically unwanted advertisements, etc.), pop-up advertisements in various websites, leaflets in the general case, and other email targeted for general promotional purposes. The user typically discards such information, but relevant messages are of recurrent nature, namely, they are repeated at frequent rates in order to achieve their goal. Sometimes users can be bothered by very frequent recurring indifferent information; however, most of the times the user cannot do much to restrict or discard them. Characteristic examples include phishing email messages and promotional/discount pop-ups are various electronic shopping websites.

We should note that although malicious and indifferent types of information are essentially of different nature in terms of context, in many occasions, their diffusion nature is identical, or at least very similar. Thus, later in this chapter, we use the same SIS infection model to study their propagation. The reader should keep in mind their diverse contextual nature and use the corresponding models appropriately given the specific application framework they emerge.

Thus, it may be observed that the various types of information disseminated through networks and humans resemble different cases of malware and epidemic diffusion. Consequently, given specific assumptions, it may be possible to model the information dissemination via malware diffusion modeling techniques. In this section, we focus especially on these cases of application of the previously proposed malware diffusion modeling frameworks on information dissemination over wireless complex communication networks. As already explained in Part 1 of the book, modern networks typically consist of various complex subnetworks [164], which eventually merge as a heterogeneous large-scale network, possibly connecting to a wired infrastructure (Fig. 9.7). This is the trend in future 5G and heterogeneous networks, where contemporary users, equipped with devices having various radio interfaces, can communicate with each other in more complicated ways than in the past and utilizing multiple subnetworks. For example, a user may communicate with another user via mobile phone over cellular networks, while also communicating with a different user in his/her geographic vicinity via WiFi [107] or Bluetooth [230]. In order to evaluate the dynamics of information dissemination (information dissemination dynamics — IDD) in such heterogeneous complex communication networks, where communications are affected by both social relations (at overlay networks, e.g. social network) and physical proximity (contacts of network nodes by exchanging packets point-to-point), novel analytical models exhibiting parameters representing IDD for different types of underlying communication networks are required. In this section, as already explained, a radical approach of using a mapping between malware diffusion and information dissemination is presented and exploited for studying the dynamics of IDD, and moreover for obtaining means to control the IDD.

In the following, we present a generic modeling framework for IDD and discuss the analogy to epidemics models for describing such dynamic operation. Within this framework, specific IDD models for different types of complex networks and assessment metrics are developed. Different analytical approaches for describing useful-information dissemination malicious/indifferent-information spreading are presented and briefly analyzed, followed by indicative evaluation results.

The main problem with all the above families of approaches and individual techniques is that typically, in most of these approaches only one type of information is considered over a specific network topology. The objective of each such approach is to spread the information to as many users as possible. However, this is not always the case in arbitrary networks, where different types of information may propagate.

Substantial works [46,60,68,231,236] have employed an analogy of IDD in a single network as infectious spreading diseases by using ODE in the field of epidemics [58,219], which could act as a quick reference to efficiently gather approximate knowledge of information dissemination speed and status with various settings of average node degrees and attain further control [47] in those networks. A more thorough summary of such protocols can be found in [4]. However, IDD are further complicated in wireless complex communication networks due to the presence of dynamic behaviors regarding the variability of topology and user behavior. Epidemic routing protocols are characterized as those randomized approaches that are based on both stochastic processes and epidemics models, such as the ones presented in [41,91,129] and references therein.

However, all such works mainly focus on specific types of information and network topology. The framework that will be presented in the following serves as one of the early attempts to systematically analyze IDD in a generic manner and allow assessing the dissemination and robustness performance in both current and future wireless complex networks and different types of information.

The main feature of this application, which is a joint application of the epidemics and queuing frameworks presented in Parts 1 and 2, 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. Consequently, there are two broad types of information, short-lived, i.e. useful information, with a short circulation lifetime and long-lived information, such as malicious information, with a longer circulation lifetime. We summarize the features of these types of information that we consider most important in Table 9.1.

To address the above, two different paradigms have been proposed that describe the behavior of systems, a SI for the first and SIS for the second type of information. Both paradigms were inspired by drawing analogies to the field of epidemics [48]. Two specific approaches have been analyzed, and the behavior of each case is demonstrated, showing how they can be used in order to identify the parameters and properties of the underlying wireless complex communication networks that govern IDD [48].

Recognizing the similarities between IDD and the spread of infectious diseases, ODE models in the field of epidemic [58,219] have been widely adopted as tools to analyze IDD in communication networks [46,60,68,204,231,236]. Since ODE models provide closed-form formulas for the performance metrics of IDD, a wide range of effects can be encompassed by aggregating individuals in the network into two states (i.e. infected and susceptible), and thus reducing computation time and required resources. In contrast, both agent-based emulation model presented in [230] and simulation experiments presented in [221] try to precisely capture attributes of individuals in the network and the interactions among them via massive experiments; thus, the appeals of analytical tractability are neglected. Obviously, the complexity of modeling individual-level details significantly increases with the number of individuals, and thus the ODE model is suitable to act as a quick tool to identify IDD in large complex networks.

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). Under this regime, users obtain information either from information sources, or from legitimate users that have already stored the information (already in the “I” state). Several works have provided epidemic-based models for such type of information dissemination in the Internet [218], and in wireless networks [9,156].

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 tough 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. For the rest of this chapter, we will focus on “malicious” information, while keeping in mind that similar models and behaviors can be obtained for “indifferent information” as well.

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. As will be seen later from the obtained results, the model and employed methodology is similar to that of Chapters 3 and 4. The main difference is that now the topology corresponds to a potentially mesh-like network, and thus the network graph can be now any of small-world (SW), scale-free (SF), regular, or other type, compared to the random geometric graph (RGG) of the previously studied distributed wireless networks case (Chapter 4).

This behavior resembles epidemics, where individuals become infected, then recover from a disease, and become susceptible again to a different or the same disease (if they do not properly “vaccinate”) — SIS model. Contrary to useful information, we notice that the SIS model defines two potential transitions between the two possible states of a user, namely, switch from susceptible to infected and then switch back to the susceptible state. This model has been also adopted in [190] for information dissemination, but again it is targeted toward only a specific type of information and network topology, as the SI epidemic models mentioned above.

By employing the aforementioned analogy to epidemics and malware diffusion, 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 to identify the impact of each topology on the IDD performance and robustness. The classification of these models will be based on the following critical parameters involved:

Connectible networks: For a network with variable connectivity, the network is (partially) connectible, if each node has a positive probability to establish an undirected connection to any other node in the network. A network with (different) same connection probability in each node is defined as (un)equally connectible. Regarding connectible networks, the probability to establish an undirected connection to any other node in the network involves a partial set of nodes in the network, not all of them.

Additional properties may be identified, capturing topological properties of the underlying complex networking infrastructures, and could be exploited for analyzing IDD in these types of 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 [164]. Based on the specific metrics, the complex networks of interest for the analysis of the IDD via malware diffusion techniques can be classified in five main categories, cumulatively depicted in Table 9.2.

Homogeneous Mixing and Partially Connectible (HoMPC): In a (regular) lattice with degree k every node connects to its k nearest neighbors [23]. A lattice is a HoMPC network since the degree distribution is a delta function with magnitude equal to 1 located at k[23]. Another example of HoMPC networks is wireless sensor networks, where sensors are uniformly and randomly distributed on a plane [202]. In the case of grid-based sensor networks, the number of neighbors in the communication radius of a sensor is fixed, which behaves exactly as a HoMPC network.

Homogeneous Mixing and Equally Connectible (HoMEC): ER random graphs [67] assume that an edge is present with probability pe for N(N−1)∕2 possible edges. The degree distribution of an ER network in relatively large networks is

Homogeneous Mixing and Unequally Connectible (HoMUC): SW networks generated by the WS model [225] are constructed from a regular ring lattice¹ with 2j edges for each node (where j is an integer number), and randomly rewiring each edge of the lattice with probability pw such that self-connections and duplicate edges are excluded. The degree distribution of a SW network is

Heterogeneous Mixing and Partially Connectible (HeMPC): M2M networks [103], wireless mesh networks [5], or smart grids have potentially nonstructured degree distributions due to finite transmission range, heterogeneity in location, mobility, channel quality variations, and time-varying user behavior, eventually classifying the underlying topology as HeMPC.

Heterogeneous Mixing and Unequally Connectible (HeMUC): A HeMUC network is a power-law distributed network, i.e. having degree distribution P(k)∼k−r, with r in the range 2≤r≤3, which is also called a SF network. Barabasi and Albert observe two essential factors of SF network: growth and preferential attachment [1]. In this model, denoted by BA, every new node connects its m edges to existing nodes according to the preferential attachment rule, and k̄b=2m. The power-law degree distribution suggests that most nodes have few neighbors, while some “supernodes” (hubs) tend to have a great amount of neighbors. Thus, the power-law distributed network can be treated as a HeMUC network.

Table 9.2 summarizes the aforementioned complex network categories. Note that the size of the largest connected component (“giant component”) is also an important measure of the effectiveness of the network at information epidemics or cooperations. Regarding this, a network is saturated if the giant component size approaches the total number of nodes in the network. Otherwise, nodes may be isolated from the giant component (nonsaturated network). For instance, a giant component emerges almost surely in random graphs, if ∑kk(k−2)P(k)>0[161].